Tesis Doc o al
A i icial In elligence in A chi ec u e
A Jou ney om Enginee ing Applica ions o Gene a i e
Design and Concep ual Rep esen a ions o Space
Realizada po
Jaime de Miguel Rod ´ıguez
Pa a la ob enci´on del ´ı ulo de
Doc o
Di igida po
Fe nando Sancho Capa ini
En el depa amen o de
Ciencias de la Compu aci´
on e In eligencia A i icial
P og ama de Doc o ado de Ingenie ´ıa In o m´a ica
2024
Dedicado a mis Pad es po su eno me paciencia,
a Fe nando Sancho po su ines imable apoyo
y a mi T´ıa T iny Rod ´ıguez-Bu gos po su dedicaci´on incansable al conocimien o.
Ag adecimien os
Quie o exp esa mi m´
as p o undo ag adecimien o a Fe nando Sancho, po
much´
ısimas cosas, pe o en especial, po habe alo ado la inno aci´
on de mi abajo
en un es ado muy incipien e, y en un momen o muy di ´
ıcil de mi ayec o ia. Sin la
con ianza que me b ind´
o el con a con su espaldo, ni es a esis, ni las apo aciones
que m´
as es imo de la misma, hubie an sido posible.
Tambi´
en a Joaqu´
ın Bo ego, po habe me dado la opo unidad de comenza
mis es udios de doc o ado en el Depa amen o de Ciencias de la Compu aci´
on e
In eligencia A i icial de la Uni e sidad de Se illa, y po habe di igido con eno me
paciencia mi p ime a e apa en el p og ama.
A Ped o Almag o, po su explicaci´
on en p o undidad del p oceso de
en enamien o de las edes neu onales en el Semina io de Ap endizaje Au om´
a ico
del depa amen o (gene osamen e o ganizado po Fe nando Sancho), la cual me
ab i´
o la pue a a comp ende muchos o os modelos que se mencionan en es a
esis.
A Ma ´
ıa Eugenia Villa a˜
ne, po habe me mo i ado y animado a acome e el
es udio de m´
e odos gene a i os pa a la usi´
on de ipos a qui ec ´
onicos, con is as a
la con e encia AAG 2018.
A An onio Mo ales, Ma ´
ıa Vic o ia Requena y Emilio Rome o, po
in oduci me en el campo de la ingenie ´
ıa s´
ısmica y po odo el apoyo ecibido
du an e los p oyec os PERSISTAH y SIMRIS.
A Ma hew Pea y, po su gene osidad en e isa mis abajos y sus comen a ios
siemp e ace ados.
A Pille Bunnell, po su se ie de ´
ıdeos Dancing Wi h Ambigui y, que ue on una
g an uen e de inspi aci´
on pa a el desa ollo del m´
e odo p opues o en es a esis sob e
la gene aci´
on eme gen e de es uc u as concep uales.
En elaci´
on al m´
e odo pa a la gene aci´
on eme gen e de es uc u as
concep uales, ambi´
en quisie a mos a mi ag adecimien o a F ancisco M´
a quez,
po sus excelen es clases sob e el mundo de la iden idad y el mundo de la di e encia.
Dichas clases despe a on mi in e ´
es po los aspec os cogni i os del dise˜
no
a qui ´
ec onico en mis p ime os a˜
nos de ca e a, y me lle a on a encon a los
abajos de G ego y Ba eson sob e los que es e m´
e odo se basa.
A Yusuke Obuchi, po demis i ica y da me las cla es concep uales pa a
i
in oduci me en el mundo la p og amaci´
on in o m´
a ica.
A Fabio G amazio, po descub i en m´
ı la u gencia po la inno aci´
on, un
econocimien o que me dio la segu idad necesa ia pa a acome e p oyec os en
disciplinas que me e an ajenas, como la In eligencia A i icial y la Ciencia
Cogni i a, p o agonis as de es a esis.
A Ena Llo e , po el camino de in es igaci´
on que eco imos jun os en la
Uni e sidad ETH de Z´
u ich, que no hubie a sido posible sin ella.
Finalmen e, un ag adecimien o muy especial a Mª Ca men Ca dona, po oda
su ayuda en la ges i´
on de ´
ami es adminis a i os y de an os apu os de ´
ul ima ho a
a lo la go de es os a˜
nos.
ii
Resumen
Es a esis explo a el papel de la In eligencia A i icial (IA) en el modelado
concep ual del espacio, cen ´
andose en la es ´
e ica a qui ec ´
onica, o enus as, y
abo dando ambi´
en u ili as ( uncionalidad) y i mi as (es uc u a). El aspec o
es ´
e ico, siendo el m´
as desa ian e, es cen al en la in es igaci´
on, que examina la
in e acci´
on en e la IA, la es ´
e ica del dise˜
no y las ep esen aciones espaciales. Se
examinan los desa ´
ıos y opo unidades que la IA p esen a pa a la c ea i idad, el
azonamien o concep ual y la ep esen aci´
on espacial: es pila es undamen ales
en el discu so a qui ec ´
onico.
Se analizan a ias ´
ecnicas de IA, incluidas las edes neu onales pa a
aplicaciones es uc u ales en ingenie ´
ıa ci il y s´
ısmica, y los modelos gene a i os
pa a el an´
alisis u bano y la b´
usqueda gene a i a de o mas no i iales. El An´
alisis
Fo mal de Concep os se in oduce como una he amien a ´
u il pa a el es udio de
da os u banos. La esis con in´
ua analizando c ´
ı icamen e los modelos gene a i os
de IA, e aluando su po encial c ea i o, su capacidad pa a sopo a
ep esen aciones complejas y ambiguas, y su idoneidad pa a ope a a un ni el
concep ual. Si bien la IA gene a i a mues a p omesas en la gene aci´
on de
soluciones de dise˜
no c ea i as, es ´
a limi ada en la ealizaci´
on de ope aciones
impulsadas po concep os, pa icula men e en compa aci´
on con los modelos
simb´
olicos, que des acan en el azonamien o, la composibilidad y la explicabilidad.
La in es igaci´
on inalmen e p o undiza en el p oblema de la ep esen aci´
on
espacial en el dise˜
no a qui ec ´
onico. Se e isan a ias ap oximaciones simb´
olicas y
neu o-simb´
olicas, aunque ninguna abo da comple amen e los complejos aspec os
cuali a i os del espacio, undamen ales pa a la cognici´
on humana y la p ´
ac ica
a qui ec ´
onica. En espues a, es a esis p opone un nue o modelo pilo o que
e isi a los en oques pu amen e simb´
olicos. Es e modelo p opo ciona una base
pa a la eme gencia de es uc u as concep uales a pa i de da os senso iales,
abo dando el p olongado p oblema del pa adigma simb´
olico en IA y o eciendo
una posible soluci´
on pa a la ep esen aci´
on de obje os espaciales en el dise˜
no
a qui ec ´
onico.
En ´
ul ima ins ancia, es a esis con ibuye al c ecien e di´
alogo en e la IA y el
dise˜
no a qui ec ´
onico al p opone un nue o ma co pa a in eg a la IA en los
p ocesos c ea i os y concep uales que de inen la disciplina. Tambi´
en o ece una
e aluaci´
on c ´
ı ica de los m´
e odos ac uales de IA y sugie e un en oque no edoso
que pod ´
ıa allana el camino pa a u u os a ances en IA y Dise˜
no.
iii
Abs ac
This hesis explo es he ole o A i icial In elligence (AI) in he concep ual
modelling o space, ocusing on a chi ec u al aes he ics, o enus as, while also
add essing u ili as ( unc ionali y) and i mi as (s uc u e). The aes he ic aspec ,
which is he mos challenging, is cen al o he esea ch, which examines he
in e play be ween AI, design aes he ics, and spa ial ep esen a ions. I examines
he challenges and oppo uni ies ha AI p esen s o c ea i i y, concep ual
easoning, and he ep esen a ion o space — h ee pilla s ha a e cen al o
a chi ec u al discou se.
Va ious AI echniques a e analysed, including neu al ne wo ks o s uc u al
applica ions in ci il and seismic enginee ing, and gene a i e models o u ban
analysis and o m- inding. Fo mal Concep Analysis is in oduced as a key ool o
concep ual modelling in AI, applied o u ban case s udies. The hesis con inues by
c i ically analysing gene a i e AI models, e alua ing hei c ea i e po en ial, hei
capaci y o handle complex and ambiguous ep esen a ions, and hei sui abili y o
pe o m a a concep ual le el. Al hough gene a i e AI shows p omise in
gene a ing c ea i e design solu ions, i is limi ed in pe o ming concep -d i en
ope a ions, pa icula ly compa ed o symbolic models ha excel in easoning,
composabili y, and explainabili y.
The esea ch inally del es in o he p oblem o spa ial ep esen a ion in
a chi ec u al design. A a ie y o symbolic and neu al-symbolic app oaches a e
e iewed, ye none ully add ess he complex, quali a i e aspec s o space cen al
o human cogni ion and a chi ec u al p ac ice. In esponse, his hesis p oposes a
no el p oo -o -concep model ha e isi s pu ely symbolic app oaches. This model
p o ides a ounda ion o eme ging concep ual s uc u es om aw senso y da a,
add essing he long-s anding symbol g ounding p oblem in AI and o e ing a
po en ial solu ion o ep esen ing spa ial objec s in a chi ec u al design.
Ul ima ely, his hesis con ibu es o he g owing dialogue be ween AI and
a chi ec u al design by p oposing a new amewo k o in eg a ing AI in o he
c ea i e and concep ual p ocesses ha de ine he discipline. I o e s a c i ical
assessmen o cu en AI me hods and sugges s a no el app oach ha could pa e
he way o u u e ad ancemen s in AI and Design.
i
Con en s
1 In oduc ion .................................. 1
1.1 B ie o e iew o Concep Theo ies . . . . . . . . . . . . . . . . . . . . 4
1.2 Concep s in A i icial In elligence . . . . . . . . . . . . . . . . . . . . . 6
1.3 Discussion.................................. 10
1.4 S uc u e o he documen . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Con ibu ions ................................ 14
1.5.1 Use-Case Speci ic Con ibu ions . . . . . . . . . . . . . . . . . 15
1.5.2 Con ibu ions o B idging AI and A chi ec u al Design . . . . 16
1.5.3 Publica ions associa ed wi h he hesis . . . . . . . . . . . . . . 17
2 Enginee ing Applica ions o A i icial In elligence in
A chi ec u e .................................. 20
2.1 Backg ound ................................. 20
2.2 Ea lywo ks ................................. 24
2.2.1 Induc i e Lea ning . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.2 Concep ual Clus e ing o Lea ning by Obse a ion . . . . . . 26
2.3 Cu en ends: Pa e n Recogni ion and Deep Lea ning in Ci il
Enginee ing ................................. 28
2.3.1 Rela edwo ks............................ 36
2.4 Expe imen al applica ion . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.1 Me hodology ............................ 41
2.4.2 Resul s................................ 58
2.5 Discussion.................................. 64
3 U ban In e mezzo I ............................. 67
3.1 In oduc ion and li e a u e e iew . . . . . . . . . . . . . . . . . . . . 67
3.2 Me hodology ................................ 69
3.2.1 P e-p ocessing ........................... 70
3.2.2 Gene a ion and augmen a ion o aining and alida ion se s 72
3.2.3 Va ia ional Au oencode model . . . . . . . . . . . . . . . . . . 72
3.3 Resul s .................................... 76
3.4 Discussion.................................. 76
3.5 Conclusions ................................. 81
4 Gene a i e A i icial In elligence in Design ............ 83
4.1 Backg ound ................................. 83
4.1.1 The connec ionis leap o wa d . . . . . . . . . . . . . . . . . . 86
4.2 Me hods ................................... 90
4.2.1 ML models as c ea i e design engines . . . . . . . . . . . . . . 91
4.2.2 Founda ion o gene a i e ML me hods . . . . . . . . . . . . . 94
4.3 Li e a u e e iew: (a chi ec u e- ela ed) . . . . . . . . . . . . . . . . . 97
4.4 Expe imen al applica ion . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.4.1 In oduc ion............................. 102
4.4.2 Me hodology ............................ 104
4.5 Expe imen a ion and discussion o esul s . . . . . . . . . . . . . . . . 114
4.5.1 Conclusions............................. 134
5 U ban In e mezzo II ............................. 137
5.1 In oduc ion................................. 137
5.1.1 U ban In o ma ional Ecosys em . . . . . . . . . . . . . . . . . 138
5.1.2 Housingma ke s.......................... 140
5.1.3 The Sel -Ci y pla o m . . . . . . . . . . . . . . . . . . . . . . . 141
5.2 Me hodology (Fo mal Concep Analysis) . . . . . . . . . . . . . . . . 143
5.2.1 Con ex s om u ban digi al oo p in s . . . . . . . . . . . . . . 144
5.3 P elimina y explo a ion . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.4 Conclusions and u u e wo k . . . . . . . . . . . . . . . . . . . . . . . 145
6 Concep ual ep esen a ion o space .................. 149
6.1 Space ..................................... 150
6.2 The Symbol G ounding P oblem . . . . . . . . . . . . . . . . . . . . . 155
6.3 Rela edwo ks................................ 157
6.4 Backg ound me hod: Fo mal Concep Analysis . . . . . . . . . . . . . 163
6.5 Expe imen al p oo -o -concep p oposal . . . . . . . . . . . . . . . . . 164
6.5.1 Me hod................................ 169
6.5.2 Expe imen a ion and esul s . . . . . . . . . . . . . . . . . . . 176
6.5.3 Compa ison o esul s . . . . . . . . . . . . . . . . . . . . . . . 179
6.5.4 Discussion.............................. 181
6.5.5 Conclusions............................. 186
6.5.6 Fu u ewo k............................. 188
7 Discussion and conclusions ....................... 195
7.1 Discussion .................................. 195
7.2 Conclusions ................................. 208
i
Bibliog aphy .................................... 210
ii
6.4 Time se ies ep esen a ion o he sample en i y . . . . . . . . . . . . . 173
6.5 Fo mal con ex able esul ing om s ep 1 . . . . . . . . . . . . . . . . 174
6.6 Resul ing concep se a e s ep 1 . . . . . . . . . . . . . . . . . . . . . 175
6.7 Concep s (in en ) p esen ac oss all cu es in he sample-se . . . . . 177
6.8 Numbe o di e ing concep s wi h pa ame e s: angle ......... 178
6.9 Numbe o di e ing concep s wi h pa ame e s: angle,wid h . . . . . 178
6.10 Numbe o di e ing concep s wi h pa ame e s: angle,x,y...... 178
6.11 Numbe o di e ing concep s wi h pa ame e s: angle,x........ 178
6.12 Numbe o di e ing concep s wi h pa ame e s: angle,wid h,x,y. . 179
6.13 Fo mal con ex able esul ing om s ep 2 . . . . . . . . . . . . . . . . 191
6.14 Fo mal con ex a e s ep 3 ( emo ed edundan in e als) . . . . . . 191
6.15 Final o mal con ex ob ained . . . . . . . . . . . . . . . . . . . . . . . 192
6.16 Concep s C10 –C28 (all emaining concep s) . . . . . . . . . . . . . . . 193
xi
1. In oduc ion
This hesis is se ou as an explo a ion o A i icial In elligence (AI) and Machine
Lea ning (ML) echniques in A chi ec u e, wi h some ouches also upon he ield
U ban S udies. O cou se, ha is an o e whelmingly b oad opic, o which dozens
o olumes can be w i en. A emp ing o deli e a comp ehensi e accoun o all
he di e en a eas wi hin he ield o A chi ec u e in which AI and ML a e playing
an impo an ole is a e y b oad ask. Ins ead, his hesis is a icula ed in a se ies
o s udies on A chi ec u e and AI, which will be used as a ehicle o wea e a
esea ch jou ney: om he domain o pa e ns o he complex and mul i ace ed
ealm o concep s. The way will be ma ked by case s udies and discussions on bo h
ends o he AI spec um: symbolic and s a is ical me hods (la gely ep esen ed by
connec ionism). And also, by combina ions o bo h, namely, neu al-symbolic
me hods, which ha e been a ho esea ch opic in ecen yea s and emain so oday.
A chi ec u e as a ield has a e y long his o y. Some ea ly accoun s o his
discipline p obably go back o he Egyp ian physicis and a chi ec Imho ep [4].
Howe e , he ea lies su i ing w i en wo k on he subjec o a chi ec u e is “De
a chi ec u a” by he Roman a chi ec Vi u ius in he ea ly 1s cen u y AD [5]. He
es ablished he h ee ounda ional p inciples o A chi ec u e: i mi as,u ili as, and
enus as (s eng h, u ili y, and beau y, espec i ely) [6]. Al hough much has
e ol ed in he ield since hen, hese p inciples s ill s and hei g ound oday in one
way o ano he ; as well as qui e a ew Roman cons uc ions (and pe haps his is no
a o al coincidence).
In ou cu en ime, i mi as co esponds o he enginee ing side o
A chi ec u e. This is a ield ha has ad anced eno mously. And maybe because i s
objec i iable and mo e clea scien i ic na u e, i is he one whe e ML has ini ially
had a g ea e impac . In pa icula , he powe o mode n neu al ne wo k models in
asks o complex mul i a ia e eg essions and pa e n ecogni ion among o he
asks has yielded a ple ho a o unp eceden ed applica ions in his ield. Fo his
eason, i mi as, oge he wi h he s udy o pa e ns and complex eg essions in
enginee ing applica ions, will be he s a ing poin o his jou ney.
Howe e , he o he wo a ibu es: u ili as and enus as, a e mo e slippe y in
e ms o scien i ic de elopmen , especially he la e . The ole o unc ion in
A chi ec u e had i s apex du ing he Mode n Mo emen (a.k.a. In e na ional S yle,
1920s – 1970s), spea headed by a chi ec s like Le Co busie , Ludwig Mies an de
Rohe, Wal e G opius, and Kons an in Melniko , among o he p ominen pionee s
1
[7]. Ano he igu e, Louis Sulli an, popula ised he amous axiom ”Fo m ollows
unc ion” [8] which called o p io i ising u ili y in a chi ec u al design, in
de imen o beau y. The pu sui o a chi ec u al beau y by i sel was owned
upon du ing his pe iod. As an example, he book “O namen and C ime” by
Adol Loos [9], was one o he mos in luen ial i les among a chi ec u al p ac ices
and schools a he ime.
Despi e he ela i ely ecen emphasis ha he ield has s owed upon unc ion,
he applica ion o AI o ML o assis he u ili as o buildings has no been
eno mously ui ul, gene ally speaking. The u h o he ma e is ha o
a e age-sized buildings, i ing a se o p og amma ic equi emen s can be equally
a ela i ely simple o ex emely complex ask. Bu in nei he case does i ha e o
in ol e a lo o da a (which is a common ma ke o he use o ML). When he ask
is simple, i is ob iously no necessa y o in ol e AI, unless he e is a need o a
so o en masse p oduc ion o designs. Con e sely, when he ask is di icul , he
complexi y is ypically d i en by he need o ind comp omises be ween
mul idimensional aspec s ha ope a e mos ly on a concep ual le el. Fo example,
an a chi ec may ha e o ind a spa ial solu ion ha p oduces a eeling o
’in imacy’, while a he same ime balancing a na u al-ligh geome y ha is
cos -e ec i e and easy o build, possibly in addi ion o a ew o he equi emen s.
In his sense, designing may be compa ed o sol ing a icky puzzle. No one wi h
many pieces, bu one wi h, so o speak, a couple dimensions o mo e added on op
o he con en ional h ee-dimensional space.
Sol ing his puzzle equi es no only a good amewo k o spa ial easoning,
bu also one ha is able o in e ac wi h o he design cons ain s. Among hem, one
may ind s uc u al pa ame e s, economic a iables and o he objec i iable aspec s;
bu also, o he s less angible, like cul u al habi s o psychological ac o s ha may
(o may no ) ende a space sui able o hose ac i i ies o which he space is
designed. In o he wo ds, he u ili y aspec s ha conce n he as majo i y o
buildings a e no as objec i e o ma hema ical as he e m unc ion may sugges .
Addi ionally, unc ion is a a he lexible e m, and i s in e p e a ion may a y
widely as a chi ec s and designe s push he bounda ies o he discipline. Howe e ,
hese nuances may be o e looked when one conside s la ge building
con igu a ions ha equi e complex p og amma ic unc ionali ies, such as
in e na ional ai po s, la ge hospi al compounds and acili ies, indus ial
manu ac u ing o p oduc ion plan s, e c. In hese cases, i is sa e o speak o
unc ion in a mo e classical and objec i e sense. The mo e hese building complexes
beha e like a sys em wi h clea objec i e cons ain s and well-de ined goals, he
g ea e hei po en ial o AI applica ions.
2
In his sense, one a ea on which u ili as has de ini ely h i ed is he ield o
U ban Analysis. G ea examples can be ound in he ea ly complex sys ems
modelling o u ban ci y g ow h du ing he 1960s and 1970s [10,11], he s udy o
ci ies as mo emen economies o Bill Hillie and Space Syn ax in [12], and he
p esence o well-es ablished jou nals ha a e iddled wi h esea ch on ci ies using
nume ous AI and ML echniques (such as Compu e s, En i onmen and U ban
Sys ems o En i onmen and Planning B: U ban Analy ics and Ci y Science). Following
his end, wo u ban s udies a e p esen ed in his hesis: U ban In e mezzo I & II.
The i s is a en masse building ypology analysis o he ci y o Se ille using
Va ia ional Au oencode s, and he second is a eal es a e analysis o he same ci y
based on Fo mal Concep Analysis (FCA) [13,14].
Bu , as al eady men ioned, dealing wi h mo e nuanced app oaches o
unc ionali y and especially, when add essing aes he ics in A chi ec u e and
Design, is qui e a challenging en e p ise. Aes he ics is a highly subjec i e domain.
Any compu a ional app oach o e en any a emp o a icula e some deg ee o
objec i i y a ound i will ace g ea di icul ies. To illus a e his poin , one may
obse e some undamen al di e ences in he way enginee ing e sus design
p ac ices a e augh in oday’s class ooms (a leas in he wes e n educa ion
sys em). While mos enginee ing asks a e based on he p inciple o op imisa ion
and inding he bes design o solu ion o a gi en p oblem, aes he ic-based design
s ands qui e on he opposi e end o he spec um: he e is ne e , as a p inciple, one
igh answe o any gi en ask.
When op imisa ion, as a c i e ion, is h own ou he window, assessing and
e alua ing a design may seem like a ha d ask (and i is indeed). Fo his eason,
among o he s, Design as a discipline has e ol ed o os e he idea o concep ual
discou se o na a i e as an in eg al pa o he c ea i e p ocess. A concep ual
na a i e [15,16] can be unde s ood as a ool h ough which designe s can explain
and make sense o hei c ea ions cohe en ly. In o he wo ds, i is a cohe en
discou se based on a concep ual unde s anding o hei c ea ion p ocess and hei
p oduced a e ac s. I has bo h a componen o sel -guidance o sel -unde s anding
as well as o communica ion ( o o he s). Wi hou going in o oo much de ail, he
e alua ion p ocess o a s uden ’s wo k in his domain o en lies in assessing he
cohe ence o he discou se p esen ed wi hin a ce ain logic amewo k. Typically, in
a u o -s uden scena io, he se o logic axioms agains which he design is
assessed is in e ed by he u o om he concep ual discou se i sel .
I is clea , he e o e, ha any compu a ional app oxima ion o Aes he ics and
Design mus es ablish a s ong heo y o concep s and concep ual ep esen a ion,
wi h an emphasis on seman ics, because ha is p ecisely he basic oolki ha hese
3
subjec s a e deal wi h in con empo a y design p ac ice. Howe e , while pa e ns
may be a p e y simple idea o unde s and, he esea ch a ound concep s is e y
he e ogeneous and mul idisciplina y. Concep Rep esen a ion cons i u es an
impo an esea ch a ea o , a leas , he ollowing ields: Philosophy, Psychology,
Neu oscience, Cogni i e Science, Linguis ics, and A i icial In elligence. And o
make ma e s e en ha de , he e is qui e a wide ange o pe spec i es e en in he
e y unde s anding o wha concep s a e [17].
Howe e , i is impo an o acknowledge ha some cu en ML models, such
as Gene a i e Neu al Ne wo ks, ha e achie ed a g ea deal in e ms o p oducing
c ea i e ou pu s (in a loose sense o he e m c ea i e). These models can compose
s unning images om ex p omp s and e en gene a e new ones om aining
expe ience. While hey ha e no been explici ly buil o suppo concep s in he
classical no ion o he e m, hei impo an achie emen s sugges ha hey should
be aken se iously in o accoun in concep s udies. As such, his olume dedica es a
ull chap e o explo ing hei po en ial o concep esea ch.
1.1. B ie o e iew o Concep Theo ies
Concep s a e one o hose no ions ha a e easy o unde s and in ui i ely bu e y
ha d o de ine o mally. Pla o and A is o le al eady heo ised abou concep s in one
way o ano he , which speaks olumes o he impo ance and his o ic legacy o he
idea o concep s. Pla o belie ed ha o e e y ca ego y o objec s in he wo ld, he e
exis ed a pu e and unco up ed ins ance o i in he wo ld o Ideas o wo ld o Fo ms
[18,19]. Ins ead, o A is o le, he wo ld was made o subs ances (which he la e
eplaced wi h he e m essence). Subs ances we e o wo kinds: p ima y subs ances
comp ised independen objec s composed o ma e and o m; seconda y subs ances
co esponded o la ge g oups o ca ego ies o which he o me objec s belonged
[20].
Since hen, he idea o a concep has been a cons an p esence in bo h
philosophical and scien i ic a enas. The eminen philosophe s Lock and Hume, o
example, we e ea ly adop e s o he Rep esen a ional Theo y o Mind (RTM) [21].
A heo y ha o da e is s ill he mos p e alen in he ield [22]. RTM posi s ha
hinking occu s in an in e nal sys em o ep esen a ion. Belie s and desi es and
o he p oposi ional a i udes en e in o men al p ocesses as in e nal symbols [21].
Howe e , his iew has impo an de ac o s ha ha e p oposed al e na i e
pe spec i es. Some o hem main ain ha concep s should be a he unde s ood as
men al abili ies [23,24,25] ( o ins ance, he concep wa e , may an amoun o
simply dis inguishing wa e om o he en i ies and d awing some in e ences om
i ), while o he de ac o s iew concep s as abs ac objec s ha media e be ween
4
language- hough and e e en s (objec s in he wo ld, eal o ic ional). The main
a gumen he e is ha a concep may exis ou side o any human mind; he e exis
concep s ha humans ha e ne e ye en e ained only because o ou in ellec ual
limi a ions [26]. Thei suppo e s also poin ou ha a ep esen a ional heo y o
mind poses he philosophical challenge ha he same concep s may ha e di e en
ep esen a ions in e e y indi idual.
Many suppo e s o he RTM a e also in a ou o wha has been called he
Theo y Theo y o Concep s [27,28]. Acco ding o his pos ula e, ca ego isa ion is a
p ocess ha s ongly esembles scien i ic heo ising. The heo y is able o explain
some o he complexi y a ound he ca ego isa ion aspec o concep s. Fo example,
child en ha e been epo ed o dismiss he impo ance o isual simila i y when
aced wi h a si ua ion whe e a dog is in en ionally al e ed o esemble a accoon.
They a gue ha e en a a young age, child en ha e a basic unde s anding o biology.
Acco ding o he heo y, being a dog goes beyond me e isual esemblance: i hinges
on possessing he essence o dogs, wha e e ha may be [29]. Ano he ad an age
hei suppo e s claim is ha i helps explain concep ual de elopmen o e ime
(concep s acqui ed in childhood ha e ol e in o adul hood). The implica ions o
his iew ha e impo an consequences o AI, because i means ha concep s a e o
an ex emely subjec i e na u e – ex emely ha d o o malise.
Ano he impo an a ea o discussion is he na i is e sus he empi icis iew,
which also has deep his o ical oo s. Na i is s, on he one hand, main ain ha he e
a e p eexis ing inna e concep s (no lea n ) and ha he mind is wi ed di e en ly
o di e en domains (e.g. pe cep ion sys ems o di e en le els o abs ac ion)
[21]. Empi icis s, on he o he hand, belie e ha he e a e ew inna e concep s (o
none a all) and ha mos cogni i e abili ies a e de eloped om simple cogni i e
mechanisms [21]. Nei he Hume no Kan , o example, suppo ed he na i is
app oach [30,31]. Howe e , he deba e became much ali e in he second hal o he
wen ie h cen u y a e Fodo ’s con ibu ions o he con e sa ion [32]. Fodo
emb aced adical na i ism claiming ha lexical concep s lack seman ic s uc u e,
and consequen ly, i ually all lexical concep s mus be inna e. In his, he only
allowed ha complex concep s can be lea n , whe e lea ning is ca ied ou by
assembly o a combina o ial p ocess. No many (i any a all) ha e aken hese
adical pe spec i es, bu no ew ha e ee alua ed hei iews on concep lea ning
a e Fodo ’s a gumen s [33,34,35,22].
A u he de elopmen wi hin he empi icis iew is he no ion o embodied
cogni ion, o he embodied mind hesis [36]. Acco ding o his app oach, he
concep o ‘wa e ’ and he wo d ’wa e ’, o example, ”acqui e meaning by in e nal
s imula ion o eenac men o he pe cep ual mo o and emo ional expe iences”
5
ha a e connec ed o seeing wa e , ouching i o hea ing i splash [37,38]. The
embodied pe spec i e conside s ha human concep s a e in luenced by he kind o
body ha an o ganism possess; because i is in hei pe cep ion, ac ion, and
emo ion sys ems whe e hese concep s a e g ounded [39,40,41]. Some impo an
au ho s like Ha nad (pos ula o o he Symbol G ounding P oblem ha will be
discussed in a la e chap e ), ha e gone so a as o sugges he eplacemen o he
idea o concep s in Cogni i e Science, o “inbo n and acqui ed senso imo o
ca ego y-de ec o s and ca ego y-names combined in o p oposi ions ha de ine and
desc ibe u he ca ego ies” [42].
Embodied cogni ion has gained a e y wide suppo among he scien i ic
communi y, especially a ound Cogni i e Science. This heo y p o ides a s ong
unde s anding o conc e e concep s ( hose wi h a clea angible e e en , e.g.: apple).
Howe e , acco ding o some au ho s, i aces impo an challenges when
a emp ing o explain abs ac ones ( hose wi hou a clea angible e e en , e.g.:
lo e) [17]. Thei eason o his p oblem is ha abs ac concep s a e no only
ancho ed in he senso ial domain. In ac , hey a gue, linguis ic and social aspec s
play a key ole in he acquisi ion o abs ac concep s. Subsequen ly, hey p opose
o ex end he embodied app oach o include linguis ic and social expe iences. O
cou se, pa o his ealisa ion is due o he apid success o he dis ibu ional
seman ic hypo hesis [43]. This iew posi s ha meaning is compu ed s a is ically.
Meaning is gi en by he cooccu ence o wo ds in la ge masses (co po a) and i
de i es om he ela ionship be ween associa ed wo ds a he han be ween wo ds
and hei e e en s. I goes wi hou saying ha he ecen de elopmen o La ge
Language Models (LLM) [44,45,46] is deeply impac ing he pe spec i es on
abs ac concep lea ning.
1.2. Concep s in A i icial In elligence
In A i icial In elligence and Machine Lea ning, se e al concep heo ies ha e been
p esen ed o e he yea s. The ea ly cybe ne icians such as Wiene e e ed o he
no ion o uni e sals o cap u e “wha makes a squa e a squa e” [47]. The
connec ionis a enue g a i a ed mo e owa ds unde s anding concep s o
uni e sals as pa e ns. Pa e n ecogni ion gained eno mous ac ion, exhibi ing
e y powe ul esul s, bu was limi ed o he dis ibu ion o aining da a and
acing impo an challenges in e ms o explainabili y and composi ionali y.
Howe e , mos app oaches o concep lea ning ha e been p oposed om he poin
o iew o symbolic AI, ypically ocussing on seman ics [48]. A good e iew o
hese app oaches is discussed in he wo k o Goguen [49], which includes he
Geome ical Concep ual Spaces o G¨
a den o s, he Men al Spaces o Fauconnie ,
6
he In o ma ion Flow o Ba wise and Seligman, he Fo mal Concep Analysis
(FCA) o Wille, he La ice o Theo ies o Sowa, and he Concep ual In eg a ion o
Fauconnie and Tu ne . Nex we ocus on FCA, Men al Spaces and Concep ual
Spaces, as hey a e he mos inline wi h he subjec a s ake.
Fo mal Concep Analysis iews concep s as knowledge uni s and ac s o
cogni ion ha a e po en ially independen o language [50]. In o mal e ms,
concep s a e bina y ela ions be ween objec s and hei p ope ies. The concep
apple, o example, is de ined by (i) he symbolic p ope ies o apples (e.g.: is a ui ,
g ows in ees, has ligh colou inside, has hin skin, e c.) and (ii) all he objec s ha
e i y hose p ope ies (all apples). F om his de ini ion, and bo owing om
La ice Theo y and O de ed Se s Theo y [51,52], Wille is able o gene a e o mal
s uc u es ha exp ess hie a chical ela ionships among concep s. Addi ionally,
FCA p o ides a powe ul engine capable o easoning abou objec s and hei
p ope ies upon he de ini ion o a o mal con ex (a se o objec s and hei
p ope ies). The simplici y and ma hema ical elegance o his heo y ha e gi en i a
ela i ely la ge success, and esea ch on FCA is s ill s ong in he cu en li e a u e.
Impo an ex ensions o Rough Se s [53], Fuzzy Logic [54] o G anula Compu ing
[55] ha e been p oposed since. In addi ion, a wide a ie y o applica ions ha e
been de eloped h oughou he yea s [56,57,58,59].
Wille’s mo i a ions wen a beyond he ealm o Ma hema ics. The main
aspi a ion o his body o wo k was o suppo a ional communica ion in humans.
As such, a g ea e o was dedica ed o con ex ualising FCA in b oade
philosophical discussions and ad ances in psychology a ha ime. In pa icula ,
Wille a ibu ed o Piage ’s ounda ional wo k on cogni ion and Seile ’s ideas
con ained in “Concei ing and Unde s anding” [60]. Fu he mo e, in [50], he gi es
a de ailed accoun o FCA compa ibili y wi h Piage ’s school o hough . In
pa icula , Wille suppo s Piage ’s iew ha concep s a e nai e and subjec i e
heo ies ha con ain implici and explici assump ions abou he wo ld. In
addi ion, he au ho endo ses he no ion ha concep s a e o an abs ac and
idealising na u e, o ha “concep s conside hings and e en s ou o a speci ic
pe spec i e and econs uc only hose aspec s and ela ions which ollow om he
speci ic iew”. Despi e e o s, he impac o FCA on cogni i e science has been
mode a e. Pe haps, one o he easons is ha , while i may well be compa ible wi h
some impo an cogni i e heo ies, i ce ainly does no p o ide any explana ion
o many o he p essing ques ions and complexi ies a ound concep s discussed in
he p e ious sec ion.
Fauconnie ’s model o Men al Spaces [23] and o cogni ion in gene al, is
ex emely in e es ing. His mo i a ion was o o e come he limi a ion o
7
P oposi ional Logics in he s udy o language and cogni ion: “Rega dless o
whe he p oposi ions play a ole in seman ic heo y o na u al language logic,
sen ences a e no ca ie s o p oposi ions” [23]. He a gued ha his model was
lawed and ha a mo e lexible app oach had o be pushed o wa d, hus his
p oposal o he men al spaces model. In his iew, i seems ha he idea o concep
is no o pa icula in e es , a leas no in a monoli hic o s a ic way. He a gues
ha , con a y o wha had been he no m in linguis ic esea ch so a , meaning is
no con ained in seman ic objec s (e.g. wo ds, sen ences). Ins ead, meaning is
c ea ed in he mind ad hoc om a complex p ocess in which many ac o s in e ene,
such as con ex , p e ious expe ience, e c. In his p ocess, language is a igge o a
ehicle ha can guide and in luence he cons uc ion o meaning [61] bu , in no
case, meaning is con ained in language i sel . This pe spec i e implies ha
concep s a e highly dynamic and con ex ual. The e o e, he pu sui o de ining
concep s in a so o essence-d i en manne (wha makes a squa e a squa e), is seen
as misguided in he ligh o his wo k.
Men al Spaces as a model, howe e , has no had pe haps all he impac i
dese ed. On he one hand, Fauconnie does no p o ide a ma hema ical
o malisa ion like FCA, which makes i ha de o adop by he AI communi y. And,
on he o he hand, he model was a he complex in e ms o he numbe o
elemen s and special heo e ical ins umen s ha con o med i . This aspec leads o
a ce ain le el o a bi a iness when i is no suppo ed by empi ical e idence om
psychology o neu oscience. In ac , mos o his app oach s emmed om he ield
o linguis ics. Subsequen ly, many o he ideas a ound Men al Spaces had a limi ed
legacy in Cogni i e Science. Con e sely, his la e wo k on Concep ual In eg a ion
(o Concep ual Blending) wi h Tu ne [62] did p omp qui e some olumes o
li e a u e. The Concep ual Blending Theo y posi s ha he mind has a c ea i e
abili y o combine dispa a e elemen s om di e en domains, leading o he
eme gence o unique, in eg a ed men al spaces known as blends. As he au ho s
claim, blends allow o he gene a ion o no el meanings and insigh s. I mus be
c edi ed ha his line o esea ch is s ill e y much ali e oday, especially in he
ields o Linguis ics and C ea i i y [63,64,65,66].
G¨
a den o s’ Concep ual Spaces [67] do no eally all unde he ca ego y o
symbolic me hods. In his wo k, he poin s ou he weaknesses o bo h symbolic and
connec ionis models. Symbolic models all p ey o he F ame P oblem [68,69,70].
The upsho o his p oblem is ha p oposi ional ep esen a ions a e no well sui ed
o ep esen ing causal connec ions o dynamic in e ac ions. Addi ionally,
symbolic models ace he Symbol G ounding P oblem (SGP) o mula ed by
Ha nad [71]. The SGP manda es ha symbols should be gi en con en ( e e en s) in
a so o sel -eme gen p ocess, and no by some deus ex machina p ocedu e (e.g.,
8
expe s assign meaning o alues o he symbols). G¨
a den o s e e s o
connec ionis models as a pa icula case o associa ionism [72] (g ea ly p omo ed by
Locke and Hume), based on neu al ne wo k a chi ec u es. The main issues he
poin s ou a e (i) he need o la ge aining se s, (ii) lack o explainabili y, (iii) poo
c oss-domain pe o mance (a ne wo k canno easily gene alise wha i has lea n
om one domain o ano he , o example om audio inpu o image inpu ) and (i )
simila i ies among pa e ns lea n by he ne wo ks canno be es ablished
in insically o in a na u al way.
Concep ual Spaces, hus, a e o mula ed as a hi d way. This hi d way is a
geome ical o m o ep esen a ion (nei he symbolic no connec ionis ), whe e
concep s a e egions in a mul idimensional space. Each dimension o his space
co esponds o some domain quali ies o he wo ld. Fo example, when ocussing on
an objec colou , one may conside h ee domain quali ies: hue,sa u a ion and
b igh ness. The e o e, concep s in his space a e de ined by olume ic egions
wi hin a h ee-dimensional space de ined by hose domain quali ies. Wi h his
se up, i is clea ha he me hod is well posi ioned o g ound concep s in
pe cep ual da a. Also, he accoun s o simila i ies among concep s a e na u al o
he sys em. Addi ionally, because concep s a e egions in space, i is possible o
es ablish spa ial ela ions among concep s: hie a chical (a egion inside ano he
egion), in e sec ions, o mo e gene ally, any ela ion gi en by a de ini ion o a
egion connec ion calculus [73].
In o de o disc e ise he domain quali y space in o conc e e concep - egions,
G¨
a den o s bo ows he idea o p o o ypes om P o o ype Theo y in he line o
Quine [74]. Acco ding o a leas some aspec s o his heo y, concep s (usually)
show g aded membe ship. This means ha some e e en s a e mo e ep esen a i e
o he concep han o he s, hence he no ion o p o o ype o p o o ypical e e en (o
p o o ypical poin in he domain quali y space). F om hese poin s, Concep Spaces
sugges gene alised Vo onoi essella ion o disc e ise he space in o ini e
concep - egions. F om his s a egy, i seems appa en ha he ask o deciding
which a e he p o o ypical quali ies o a concep is no an easy one. Unless an
explici sel -eme gen mechanism is p o ided o accoun o he selec ion o
p o o ypical e e en s, i seems ha he me hod would s ill ace impo an
challenges wi h ega ds o he SGP.
The angle o Concep Spaces is pe haps no one ha has a ac ed oo much
a en ion om Cogni i e Science, al hough he au ho does h ow in some hin s a
biological and psychological esea ch ha sha e a simila geome ic app oach
[75,76]. Indeed, he me hod, as he himsel explains, is ocused exclusi ely on
cons uc i e aspec s o cogni ion a he han explana o y ones. Howe e , as a
9
hidden pa e ns om he da a, enabling ac ionable insigh s o u ban
planning agencies.
A chi ec u al Design:
• P oposes a pa ame ic da a augmen a ion scheme o h ee-dimensional
geome ic samples. And also, a speci ic ep esen a ion scheme o wi e ame
building s uc u es wi h applica ion in neu al models.
• Demons a es a o m- inding me hodology o c ea e no el building s uc u es
by combining ea u es o o he building ypologies.
1.5.2 Con ibu ions o B idging AI and A chi ec u al Design
This esea ch makes signi ican s ides in he b idge be ween AI and a chi ec u al
design, ocusing on concep ual models. I builds he case o he impo ance o
concep s in bo h design discou se and c ea i i y. And i discusses he s a e o he
a a ound concep s om he angle o Cogni i e Science and also o m he
s andpoin o o mal AI implemen a ions and gene a i e ML me hods. In
gene a i e AI, i c i iques cu en me hods unde he lens o c ea i i y and hei
abili y o pe o m a a concep ual le el, explo ing hei sui abili y o design
disciplines. Mos p o oundly, he hesis p oposes a new concep ual model o
spa ial ep esen a ion ha in eg a es pe cep ion and seman ic s uc u es, add esses
he Symbol G ounding P oblem, and pa es he way o he de elopmen o an
AI-based language o concep ual modelling. These con ibu ions ep esen a new
app oach o using a i icial in elligence in concep ual, c ea i e p ocesses cen al o
a chi ec u al design.
The main con ibu ions in his a ea a e summa ised below, dis inguishing hose
coming om he me hod p oposed a he end o Chap e 6(BIGA) om he mo e
gene al ones:
Gene al con ibu ions:
• P o ides a c i ical discussion on he cu en gene a i e AI models in ela ion
o he subjec o c ea i i y.
• O e s a su ey o gene a i e AI me hods, especially in connec ion o design
disciplines.
• Deli e s an analysis on gene a i e models h ough he lens o hei sui abili y
o pe o m unde a concep ual pa adigm.
Speci ic con ibu ions om he BIGA model:
16
• In eg a es pe cep ion and concep ual s uc u es. The me hod p o ides a
seamless in eg a ion be ween senso y pe cep ion and seman ic concep ual
s uc u es wi hou he need o combine sepa a e AI pa adigms,
dis inguishing i om neu al-symbolic models.
• Elimina es da a labelling and ex ensi e aining. I emo es he equi emen
o ex ensi e da a labelling and aining, making i mo e accessible o
p ac ical applica ions and educing eliance on esou ce-hea y AI aining
me hods.
• Enables explainable AI. By o e ing ull explainabili y o how concep s a e
o med om aw da a h ough a omic compa isons, he me hod enhances
anspa ency in AI decision-making, con ibu ing o he b oade e o o
make AI sys ems mo e in e p e able.
• Add esses he Symbol G ounding P oblem. The model’s bo om-up app oach
o cons uc seman ic s uc u es om basic okens con ibu es owa d sol ing
he long-s anding Symbol G ounding P oblem in AI.
• Lays he ounda ion o a new AI language. The me hod hin s a he po en ial
o building a basic AI language om p imi i e okens, o e ing a no el
di ec ion o u u e explo a ion in AI-d i en seman ic ep esen a ion.
1.5.3 Publica ions associa ed wi h he hesis
In a mo e b oade sense, he hesis also examines he ollowing aspec s —cu ing
ac oss bo h he connec ionis and he symbolic pa adigms in AI, and add essing he
backg ound con ex s o c ea i i y, space and design:
• C i ical Analysis o Gene a i e AI: The hesis p o ides a de ailed examina ion
o he ole o gene a i e AI in c ea i i y and design, highligh ing i s po en ial
and limi a ions.
• E alua ion o Symbolic Me hods: FCA’s applica ion in u ban analysis and i s
concep ual capabili ies a e c i ically assessed, e ealing bo h s eng hs and
a eas o imp o emen .
• In eg a ion o NSMs: The explo a ion o NSMs o e s insigh s in o how
combining symbolic and connec ionis app oaches can add ess some o he
cu en challenges in AI.
• No el Rep esen a ion Scheme: The p oposed me hod o concep ual
ep esen a ion o space in oduces a new app oach o in eg a ing senso y
da a wi h seman ic s uc u es, pa ing he way o u u e esea ch and
17
applica ion in a chi ec u al design.
In gene al, his hesis unde sco es he impo ance o in eg a ing di e se AI
app oaches o add ess he complexi ies o a chi ec u al design. I highligh s he
need o con inued explo a ion o hyb id models and no el me hods o enhance
he in e play be ween AI, c ea i i y, and human cogni ion in shaping he
a chi ec u al design discou se. Fu u e esea ch should ocus on expanding hese
me hods, explo ing hei p ac ical applica ions, and u he b idging he gap
be ween AI and he quali a i e aspec s o design.
Finally, hese con ibu ions ha e been made accessible o he esea ch
communi y h ough he ollowing publica ions (in ch onological o de ):
•de Miguel-Rod ´ıguez J,Gal´an-P´aez J,A anda-Co al GA,Bo ego-D´ıaz J.
U ban knowledge ex ac ion, ep esen a ion and easoning as a b idge om
Da a Ci y owa ds Sma Ci y. In: P oceedings o he 2016 In e na ional IEEE
Con e ences on Ubiqui ous In elligence & Compu ing, Ad anced and T us ed
Compu ing, Scalable Compu ing and Communica ions, Cloud and Big Da a
Compu ing, In e ne o People, and Sma Wo ld Cong ess
(UIC/ATC/ScalCom/CBDCom/IoP/Sma Wo ld). Toulouse, F ance.
2016:968-974.
P io o he design o socio echnical a i ac s in ci ies, i seems impo an o
ex ac he quali a i e, quan i a i e opinions, sen imen , and eedbacks
p esen in hese da a. This pape p esen s h ee solu ions o mining hese
con en s h ough Knowledge Ex ac ion me hods, as a p e ious s ep o he
p ospec ion o new sma se ices.
•de Miguel-Rod ´ıguez J,Villa a˜ne M-E,Piˇsko ec L,Sancho-Capa ini F.
Gene a ion o geome ic in e pola ions o building ypes wi h deep
a ia ional au oencode s. Design Science. 2020;6:e34. doi:10.1017/dsj.2020.31
This wo k p esen s a me hodology o he gene a ion o no el 3D objec s ha
esemble wi e ames o building ypes. These esul s om he econs uc ion
o in e pola ed loca ions wi hin he lea n dis ibu ion o a ia ional
au oencode s (VAEs), a deep gene a i e machine lea ning model based on
neu al ne wo ks.
•de-Miguel-Rod ´ıguez J,Mo ales-Es eban A,Requena-Ga c´ıa-C uz M-V,
Zapico-Blanco B,Sego ia-Ve jel M-L,Rome o-S´anchez E,
Ca alho-Es ˆe ˜ao JM. Fas Seismic Assessmen o Buil U ban A eas wi h he
Accu acy o Mechanical Me hods Using a Feed o wa d Neu al Ne wo k.
Sus ainabili y. 2022; 14(9):5274. h ps://doi.o g/10.3390/su14095274
18
This pape p esen s a no el en-masse me hod o assess he seismic
ulne abili y o u ban a eas swi ly and wi h he accu acy o mechanical
me hods. The co e o his me hodology is he calcula ion o he capaci y
cu es o low- ise ein o ced conc e e buildings using neu al ne wo ks,
whe e no building modelling is equi ed.
•de Miguel-Rod ´ıguez J,Sancho-Capa ini F. A Recu si e Ba eson-Inspi ed
Model o he Gene a ion o Seman ic Fo mal Concep s om Spa ial Senso y
Da a. a Xi . Published online 2023. doi:10.48550/a Xi .2307.08087. A ailable
om: h ps://a xi .o g/abs/2307.08087.
This pape p esen s a new symbolic-only me hod o he gene a ion o
hie a chical concep s uc u es om complex spa ial senso y da a. The
app oach is based on Ba eson’s no ion o di e ence as he key o he genesis
o an idea o a concep .
•de Miguel-Rod ´ıguez J,Sancho-Capa ini F. A Ba eson-Inspi ed Model o
he Gene a ion o Seman ic Concep s om Senso y Da a. AI Communica ions.
2024; ARTICLE IN PRESS (cu en ly unde going i s second e iew a e
ha ing submi ed a majo e ision).
This pape e isi s symbolic-only app oaches by in oducing a new algo i hm
o c ea e hie a chical concep s uc u es om spa ial senso y da a. The me hod
is based on Ba eson’s idea o di e ence as he undamen al elemen o concep
o ma ion.
•de Miguel-Rod ´ıguez J,Mo ales-Es eban A,Requena-Ga c´ıa MV,
Rome o-S´anchez E. Au oma ed Ex ac ion o Building Typologies om a
Digi al Land Cadas e Using a Va ia ional Au oencode . Wo ld Con e ence on
Ea hquake Enginee ing, Milan, I aly. 2024; ARTICLE IN PRESS (pending only
publica ion).
This pape in oduces a no el me hod o au oma e he iden i ica ion o
building ypologies om he digi al land cadas e o he ci y o Se ille,
elimina ing he need o human in e en ion. The me hod is based on a
a ia ional au oencode ha lea ns o ex ac hese ypologies wi hou
explici supe ision.
19
2. Enginee ing Applica ions o A i icial In elligence
in A chi ec u e
2.1. Backg ound
Be o e he wide sp ead o Deep Lea ning in Machine Lea ning, he ini ial
app oaches o i s applica ion in ci il enginee ing we e mos ly o ien ed owa ds
Expe Sys ems. These sys ems we e ega ded as some o he i s applica ions o
AI ha ac ually achie ed some impo an p ac ical esul s [92,93]. In he wo ds o
Dana S. Nau, expe sys ems a e “p oblem-sol ing compu e p og ams ha can
each a le el o pe o mance compa able o ha o a human expe in some
specialised p oblem domain”. Gi en his de ini ion, he di e ence om a s anda d
compu e p og am may no become appa en . Howe e , he e is an impo an
di e ence, in ha expe sys ems employ a knowledge base ha is a icula ed as a
sepa a e and independen en i y. This knowledge base, in u n, is accessed and
ope a ed by a con ol sys em ha is also a sepa a e and independen module.
Fo me ly, he p ocess o knowledge acquisi ion equi ed o o m he
knowledge base in ol ed consul ing expe s on domain ma e s. This p ocess had
a numbe o p oblems, such as communica ion wi h expe s, quali y o expe ise,
con lic ing expe ise among di e en expe s, o misunde s anding ins uc ions,
among o he s [94]. Fo many, he knowledge acquisi ion p ocess had become he
single mos impo an challenge acing expe sys ems, in wha became known as
he knowledge acquisi ion bo leneck. In his con ex , ML me hods appea ed as a
powe ul al e na i e ha had he po en ial o elimina e he a o emen ioned
p oblems. These echniques posed a huge ad an age in ha hey made
subs an ially ewe assump ions abou he da a. The iew was ha ML can be used
as a means o au oma e he gene a ion o knowledge o i s ope a ion wi hin expe
sys ems [1,95].
This au oma ed knowledge elici a ion p ocess was ini ially also e e ed o
o en as Machine Induc ion [96], because knowledge was buil by cap u ing
high-le el ela ionships om a se o obse able samples. This knowledge would
hen be applied o unseen si ua ions. Howe e , soon mo e au oma ed echniques
began o be used and he e m ell ou o ogue in a ou o he cu en and mo e
gene al one, Machine Lea ning.
Some ea ly classi ica ions o he ML app oaches a ailable o au oma ing he
20
knowledge acquisi ion p ocess include:
• Lea ning om examples, also known as Induc i e Lea ning o Concep Lea ning.
• Lea ning by obse a ion, also known as Concep ual Clus e ing o Concep
Fo ma ion.
• Theo y-d i en lea ning.
• Lea ning by disco e y [95].
Al hough classi ica ions a y acco ding o he au ho and may also seem qui e
obsole e oday, hey o e his o ical insigh in o he ea ly s ages o AI applica ions in
he ield o enginee ing.
Acco ding o he au ho s o his classi ica ion, induc i e lea ning in ol es he
acquisi ion o ’concep s’ a he high le el in he o m o decision ules and ees.
Lea ning by obse a ion, in u n, e e s o he abili y o p oduce ‘ heo ies’ ha
accoun o a se o gi en ac s o obse a ions. The di e ence wi h induc i e
lea ning is ha he e he aim is o a i e a a easoning engine ha can be applied o
he obse able wo ld, no beyond. In induc i e lea ning, he aim is o ex apola e
he indings o unobse ed si ua ions. O cou se, his dis inc ion is a he a i icial
and in p ac ice, concep o ma ion echniques such as FCA can also be applied o
new unobse ed si ua ions in an induc i e ashion. In con as , decision ules and
ees can also be used o engage in some le el o easoning o ‘ heo ising’ abou he
obse able wo ld.
Mo ing o wa d, heo y-d i en lea ning, as i s name sugges s, in ol es he
lea ning o concep ual knowledge di ec ly om a o mal domain heo y. Because i
is no common o such o mal heo ies o be a ailable in many o he a eas whe e
ML is applied in enginee ing and elsewhe e, his g oup may no ha e accoun ed
o a b oad esea ch adop ion. Finally, lea ning-by-disco e y is desc ibed as an
app oach in which knowledge is acqui ed by unde s anding o mining ce ain
pa e ns o egula i ies in he da a o among pas p oblem sol ing expe iences.
Di e en au ho s ha e added mo e ca ego ies, such as causal lea ning,lea ning by
analogy, o lea ning by expe imen a ion. O he ca ego ies also include simila i y-based
lea ning and explana ion-based lea ning [97].
In gene al, he dis inc ions be ween hese g oups a e o en qui e loose and
p esen impo an o e laps. E en mo e con empo a y classi ica ions o ML
me hods, like supe ised e sus unsupe ised me hods o symbolic e sus
p obabilis ic, can be ound o be excessi ely igid in ce ain cases (e.g.,
low-supe ision models, connec ionis easoning models, e c.). The e o e, i migh
be mo e cohe en o ocus on he indi idual me hods hemsel es a he han
21
a emp ing o ollow such classi ica ions oo closely. In he nex sec ion, some o
hese me hods will be explo ed u he .
Du ing he eme gence o ML o expe sys ems, some e o s ha e been made
o p o ide uni ied amewo ks o guide enginee s in hei implemen a ion. In [1],
Reich poin s ou wo impo an challenges p esen in he applica ions o ML o he
ield o ci il enginee ing. Fi s ly, p ac ical p oblems a e o en oo complex o be
handled by a single me hod. This ci cums ance led o he de elopmen o
mul i-s a egy lea ning [98,99]. Fo example, empi ical lea ning gene ally elies on
nume ous inpu examples while equi ing minimal backg ound knowledge. In
con as , explana ion-based lea ning equi es only a single example, bu equi es
comp ehensi e backg ound knowledge. Lea ning by analogy hinges on ha ing
backg ound knowledge analogous o he inpu . Real-wo ld applica ions a ely
mee he c i e ia o single-s a egy lea ning app oaches. Hence, he e has been a
g owing in e es in cons uc ing sys ems ha use a ious lea ning s a egies.
Wi hin hese s a egies, mac o and mic o app oaches a e dis inguished. The mac o
app oach in ol es he in e ac ion o di e en lea ning p og ams unde he
non- i ial esponsibili y o he use o manage hose in e ac ions. The mic o is
a ge ed owa ds speci ic ine-g ained asks.
Secondly, he o he di icul y ha had become appa en was ha ML
implemen a ion in ci il enginee ing and ela ed p ac ices was no as
s aigh o wa d as aking an ML p og am and applying i o he da a. Indeed, he
p ocess in ol es aligning he scope o applicabili y o ML ools wi h he speci ic
na u e o he ask a hand. This alignmen equi es a deep g asp o ML echniques
and he abili y o be c ea i e a ound hem. To assis in his challenging endea ou ,
he au ho p oposes a se en-s ep schema s a ing wi h (1) p oblem analysis, (2)
da a collec ion and knowledge, (3) p oblem ep esen a ion, (4) me hod selec ion,
(5) pa ame e se ings, (6) e alua ion and in e p e a ion, and (7) solu ion
deploymen (see Fig. 2.1). These s eps a e me ely in o ma i e o cou se, and such
guidelines end o p oli e a e o e ime wi h di e en a ia ions and scopes
depending on he inclina ion o a ce ain line o ML app oaches, o on he
applica ion domain, e c.
In a much mo e ecen publica ion [100], aimed a he heal hca e indus y, o
example, he au ho s p opose a simple ou -s ep schema: (1) incep ion, (2)
p epa a ion, (3) de elopmen , and (4) in eg a ion. Clea ly, esea ch-o ien ed
app oaches do no accoun o aspec s such as in eg a ion wi h a la ge so wa e
a chi ec u e o in e ac ions wi h use s a e deploymen as much as
indus y-d i en app oaches, which is expec ed. Ano he ecen pape [101], mo e
o ien ed owa ds supe ised lea ning, p oposes a se o i e s eps: (1) jus i ica ion
22
Figu e 2.1: Diag am o Machine lea ning applica ion s eps. Image ex ac ed om [1].
o using ML app oaches, (2) da a collec ion, (3) da a p ep ocessing, (4) ML
modelling and aining, and (5) sys em es ing and pe o mance alida ion. I can
be no ed ha , in his schema, da a- ela ed aspec s play a majo ole, as is common
in cu en ML models ha ope a e on massi e olumes o da a. As a wo king
guideline, combining he spi i o hese and o he ecommenda ions om he
li e a u e, a gene ic amewo k may be p oposed as ollows:
1. P elimina y analysis
2. Da a enginee ing
3. Me hod selec ion (model selec ion)
4. T aining, pa ame e and hype pa ame e s
5. Tes ing, in e p e a ion and e alua ion
6. Deploymen and in e ac ion
23
As an example, he case s udy p esen ed in his chap e ollows his amewo k
o a g ea ex en . I s a s wi h a p elimina y analysis, iden i ying he need o apid
u ban seismic assessmen and he cos /accu acy ade-o associa ed wi h
adi ional mac oseismic me hods. The nex s ep, da a enginee ing, in ol es
p epa ing a da ase based on s uc u al building p ope ies and seismic esponses.
Addi ionally, a da a explo a ion exe cise is also ca ied ou in his s ep. A UMAP
algo i hm (Fig. 2.10) is applied o he da a allowing o be e unde s and i s na u e
and p o iding insigh s o model selec ion. The model selec ed is a eed- o wa d
neu al ne wo k due o i s capaci y o gene alise complex pa e ns and pe o m
high-dimensional eg essions. Du ing he aining phase, he model is uned using
da a ob ained om he calcula ion o 10k s uc u es in a s uc u al analysis
so wa e (SAP2000). Du ing his p ocess, di e en model pa ame e s and
hype pa ame e s a e es ed o imp o ed accu acy. The es ing and e alua ion phase
shows he e ec i eness o he model, wi h i s p edic ions aligning closely wi h
mechanical me hods while o e ing signi ican ly as e p ocessing imes. Finally, a
po en ial o deploymen is sugges ed, posi ioning he model as a apid seismic
assessmen ool o u ban planning and disas e mi iga ion, emphasising i s
p ac ical applica ions in eme gency scena ios.
2.2. Ea ly wo ks
2.2.1 Induc i e Lea ning
Suppose N eal-wo ld obse ed examples a e gi en, {e1, . . . , eN}which a e de ined
om a se o a ibu es (p ope ies), ei= (pi1, . . . , pim), and o each o hem he e
is an obse ed classi ica ion, ci. The ask o Induc i e Lea ning is o induce om
he abo e da a a mechanism ha allows in e ing he classi ica ions o each o he
examples om he p ope ies alone. I his is possible, his mechanism could be used
o deduce he classi ica ion o new examples ha ing only obse ed hei p ope ies.
An impo an de elopmen in Induc i e Lea ning was he ID3 algo i hm
(I e a i e Dicho omize 3) de eloped by Quinlan in 1986 [96]. ID3 is a ype o
decision ee algo i hm based on Hun ’s Concep Lea ning Sys em [102] bu wi h an
In o ma ion Theo y app oach.
A decision ee consis s o a se o decision nodes (in e io ) and answe nodes
(lea es):
• A decision node is associa ed wi h one o he a ibu es and has 2 o mo e
b anches coming ou o i , each ep esen ing he possible alues ha he
associa ed a ibu e can ake. A decision node can be in e p e ed as a ques ion
24
asked o he analysed example abou one o i s a ibu es, and depending on
he answe i p o ides, he low will ake one o he ou going b anches.
• An answe node is associa ed wi h he classi ica ion o be p o ided and e u ns
he ee’s decision wi h espec o he inpu example.
I is ob ious ha ob aining a decision ee ha can p edic he examples wi h
100% eliabili y will no always be possible, bu he be e he ba e y o examples
a ailable (e.g., no con adic ions be ween classi ica ions), he be e he pe o mance
o he ee ha can be buil om hem.
Ob iously, he cons uc ion o he decision ee is no unique. By applying
di e en s a egies when deciding in which o de o ask he ques ions abou he
a ibu es, e y di e en ees may be ob ained. Also, hei cons uc ion a ies in
complexi y. Among all he possible ees, he objec i e is inding hose ha ul il
he bes cha ac e is ics as p edic ion machines. Consequen ly, he challenge is o
gi e an au oma ic mechanism o he cons uc ion o an op imal (o nea -op imal)
ee om he examples.
The ID3 algo i hm builds a decision ee om op o bo om, in a
s aigh o wa d manne , wi hou back acking, and based only on he ini ial
examples p o ided. I uses he concep o In o ma ion Gain (based on Shannon
En opy [103], which measu es he deg ee o unce ain y o a sample o examples)
o selec he mos use ul a ibu e a each s ep, and ollows a o acious me hod o
decide which ques ion o e s he highes gain a each s ep, i.e., he one ha bes
sepa a es he cu en examples om he inal classi ica ion: he lowe he
unce ain y associa ed wi h a gi en a ibu e, he close he node associa ed wi h
ha a ibu e is o he oo in he ee.
ID3 is he p edecesso o C4.5 (also known as S a is ical Classi ie ) [104], one o
he mos popula decision ee algo i hms used in classi ica ion oday. In his
ex ension, he algo i hm can handle bo h ca ego ical and con inuous a ibu es and
includes mechanisms o handle missing alues and p uning ees o a oid
o e i ing, bo h o which a e impo an limi a ions o ID3. Th oughou he 1990s,
hese wo we e he mos widely used induc i e lea ning echniques in ci il
enginee ing [105]. O cou se, o he decision ee me hods ha e also been
de eloped, such as CART (Classi ica ion and Reg ession T ees) [106], CHAID
(Chi-squa ed Au oma ic In e ac ion De ec o ) [107], and MARS (Mul i a ia e
Adap i e Reg ession Splines) [108], among o he algo i hms and a ia ions.
Random Fo es s (ensemble lea ning) we e abou o eme ge as a op playe in he
yea 2001 [109], and neu al ne wo ks had begun o gain conside able ac ion by
hen as well.
25
se up o weigh s and biases (o en ini ialised using andom alues), he
ou pu alues can be calcula ed de e minis ically using he o mula abo e
[139]. Al hough only one ou pu alue is shown in he example, i is easy o
p ojec mul iple ou pu alues in he same scheme.
Fo example, o classi ica ion asks, a ne wo k could be designed o ha e N
possible ou pu alues h ough Nneu ons in he ou pu laye . The gene al
idea is o achie e a dis ibu ion o weigh s and biases ( ainable pa ame e s)
ha when he inpu s co esponding o an example o i- h ca ego y low
h ough he ne wo k, he wo ou pu alues o m a ec o close o, say, ei( he
uni ec o in he i- h di ec ion). When all unc ions in neu ons a e
di e en iable, his can be achie ed by adjus ing he aining pa ame e s
h ough an i e a i e p ocess known as backp opaga ion. When mul iple
examples o he ca ego ies a e p ocessed by he ne wo k wi h he ensuing
adjus men o weigh s and biases, he ne wo k ’lea ns’ a dis ibu ion o
ainable pa ame e s ha minimises he classi ica ion e o . This p ocess can
be seen as a sea ch o local minima in he e o unc ion o , as commonly
e e ed o, a g adien descen along he loss unc ion.
O cou se, he e a e many di e en algo i hms o handle g adien descen , as
i is in ac one o he mos impo an ac o s in he aining p ocess, especially
in models ha ea u e a high numbe o laye s and pa ame e s. When dealing
wi h a chi ec u es wi h many laye s, hey a e known as deep lea ning models.
The e m deep lea ning is used qui e loosely in he li e a u e, wi hou a s ong
consensus on wha o how many laye s exac ly cons i u e deep lea ning. An
in-dep h discussion o his ma e can be ound in [140]. Going o wa d, his
hesis will no a emp o make any ha d dis inc ions be ween deep and non-
deep lea ning. Some o he exis ing me hods o compu e he g adien descen
will be discussed in he case s udy p esen ed a e his sec ion.
Figu e 2.4: Pe cep on scheme
32
Figu e 2.5: gene al neu al ne wo k diag am
Wi hin his gene al scheme, he e a e many di e en neu al models and
a chi ec u es possible. The mos simple, as jus desc ibed, is a Feed-Fo wa d
model. O he impo an models include Con olu ional Neu al Ne wo ks,
Recu en Neu al Ne wo ks,Au oencode s,Va ia ional Au oencode s,T ans o me s,
and Gene a i e Ad e sa ial Ne wo ks. The e a e many o he ypes and
a ia ions; howe e , hese a e a guably he main ones. In con olu ional
models [141], neu ons a e i s in e connec ed wi hin a local ange, be o e
connec ing o he nex laye . This is done o boos lea ning o ea u es ha
depend on spa ial p oximi y, as is, o example, he case in images. Recu en
models a e cha ac e ised by eeding he ou pu o a neu on back in o he
same neu on as an addi ional inpu . In his way, ecu en models a e able o
model s a e-dependan p oblems in a mo e e icien way, and a e hus
ypically chosen o lea n om dynamic sys ems ( ime-se ies). Au oencode s
[142] a e a special ype o neu al ne wo k in which, a he han ha ing a se o
ca ego ies-labelled examples, he model a emp s o econs uc he e y
same inpu being ed. The e o e, in au oencode s, he e o unc ion is simply
de ined by some measu e o he di e ence be ween he inpu and ou pu
alues, and is commonly e e ed o as econs uc ion e o . This ai makes
au oencode s a ype o unsupe ised o sel -supe ised lea ning model. They
a e usually aimed a comp ession o denoising, and no mally ea u e a
smalle -sized laye in he middle ha can be conside ed o con ain a
33
condensed encoding o he inpu s. Va ia ional au oencode s a e a pa icula
case o au oencode s ha oge he wi h gene a i e ad e sa ial ne wo ks
cons i u e a co ne s one o gene a i e AI. These models will be discussed in
he nex chap e . Finally, i is impo an o no e ha hese a e ela i ely luid
schemas, and many models a e a mix o he ypes p esen ed he e. Fo
example, i is common o in oduce con olu ional a chi ec u es in
au oencode s o a ia ional au oencode s as will be shown la e . The
ollowing is a b ie compila ion o wo ks.
Tai Ng e al. [143,144] inco po a ed an ANN wi h a Bayesian me hod o he
heal h assessmen o a s eel ame s uc u e. Radhika e al. [145] p oposed a
wa ele -based change de ec ion me hod using ANN and Suppo Vec o
Machine (SVM) o damage classi ica ion [145]. Then Ala i e al. [146]
p oposed a damage assessmen app oach based on p obabilis ic neu al
ne wo ks and Bayesian decision heo y o SHM. Lee e al. [147] designed a
heo e ical model using ANN o p edic he shea s eng h o he slende ib e
ein o ced polyme in ein o ced conc e e beams. Figuei edo e al. [148]
au ho ed an en i onmen al a iabili y s udy and damage de ec ion using
ANN, Mahalanobis dis ance, and singula alue decomposi ion. Yan e al.
[149] implemen ed a neu al ne wo k and SVM model o assess damage in
beams on ocean pla o ms. Pa sad e al. [150] applied a neu al ne wo k
model o he p edic ion o comp essi e s eng h in sel -compac ing and
high-pe o mance conc e e. And Cha e jee e al. [151] de eloped a
mul i-objec i e gene ic algo i hm o he calib a ion o a neu al ne wo k
model in he classi ica ion o ein o ced conc e e buildings. Dai e al. [152]
designed a wa ele SVM-based neu al ne wo k me amodel o eliabili y
analysis in a ious s uc u es. Finally, Bu che e al. [153] used ANN and
ex eme lea ning machine me hods o SHM in conc e e s uc u es wi h mesh
ein o cemen . Sa ka e al. [154] used CNNs o cha ac e ise c ack damage in
composi e ma e ials. Abdeljabe e al. [155,156] employed one-dimensional
CNNs o ib a ion-based s uc u al damage de ec ion, lea ning di ec ly om
accele a ion da a. Abdeljabe e al. [157] in oduced a nonpa ame ic damage
iden i ica ion me hod using CNN, e ec i e wi h only wo measu emen
sessions. Cha e al. [158] implemen ed a deep lea ning ne wo k o de ec
conc e e c acks in unnels wi hou compu ing de ec ea u es, obus
compa ed o adi ional me hods. Lee e al. [159] explo ed deep lea ning
models and CNNs o s uc u al analysis o a en-ba plana uss, showing
e iciency compa ed o con en ional neu al ne wo ks. Finally, in [160], CNN
was used o iden i y s uc u al damage, disco e ing unknown ela ionships
be ween measu emen s and damage pa e ns.
34
4. O he me hods: Zhou e al. [161] in oduced a damage de ec ion echnique
using cosine simila i y measu e. Zhang e al. [162] con ibu ed a s uc u al
iden i ica ion me hod employing pa e n ecogni ion and suppo ec o
eg ession (SVR). Lao y e al. [163] de eloped a me hodology o p edic
na u al equency esponses o a suspension b idge using mul iple linea
eg ession, ANN, SVR, eg ession ee and andom o es . Naga ajaiah e al.
[164] s udied damage de ec ion based on spa se and low- ank da a s uc u es
o s uc u al dynamics, and Yang e al. [165,166] analysed eco e y o
s uc u al ib a ion esponses and damage localisa ion wi h low- ank ma ix
decomposi ion. Yepes e al. [167] p oposed a mul i-objec i e op imisa ion o
high-s eng h ein o ced conc e e beams using Minkowsky me ics.
Ga cia-Segu a e al. [168] implemen ed a eliabili y-based op imisa ion o
pos - ensioned conc e e box-gi de b idges unde co osion a ack. Sa idemi
[169] employed gene ic algo i hms o de e mine he ensile s eng h spli
om he comp essi e s eng h o conc e e. Yeh e al. [170] implemen ed a
gene ic ope a ion ee o p edic he comp essi e s eng h o
high-pe o mance conc e e, while Cheng e al. [171] de eloped a gene ic
weigh ed py amid ope a ion ee o he p edic ion o comp essi e s eng h
in high-pe o mance conc e e. Ki emidjian e al. [172,173] u ilised
au o eg essi e models o s uc u al heal h moni o ing (SHM) o b idge
s uc u es, while Gul e al. [174] and Yao e al. [175] used au o eg essi e
models wi h a Mahalanobis dis ance-based ou lie de ec ion algo i hm o
damage de ec ion in ci il s uc u es.
As men ioned abo e, seismic enginee ing is a ield wi h ema kable
complexi ies in ol ed. The inhe en unp edic abili y o seismic e en s,
coupled wi h he in ica e na u e o s uc u al esponses, poses signi ican
challenges. Because o his, he e is an impo an window o oppo uni y in
using ML me hods o add ess hese challenges. Using he powe o ML,
enginee s can analyse as amoun s o da a, unco e pa e ns, and make
p edic ions ha we e p e iously una ainable h ough adi ional me hods.
Many au ho s and he enginee ing communi y ha e ecognised his po en ial
and ha e s a ed o wo k in ensely on ML applica ions o seismic
enginee ing.
Following his end, his chap e in oduces a neu al ne wo k applica ion
designed o p edic he seismic ulne abili y o a la ge numbe o buildings based
on simple geome ic pa ame e s. This app oach aims o s eamline he assessmen
p ocess, p o iding apid and accu a e p edic ions o he s ess-de o ma ion cu es
o building s uc u es unde seismic ac ions. De eloping as and eliable me hods
o ob ain hese cu es (capaci y cu es in seismic enginee ing lingo) can
35
signi ican ly imp o e p epa edness and mi iga ion s a egies o alle ia e he
impac o ea hquakes in u ban se ings. Be o e del ing in o he speci ics o his
applica ion, a se ies o wo ks ela ed o ML applica ions in seismic enginee ing is
p esen ed. These s udies unde sco e he p og ess and po en ial o in eg a ing ML
in o he ield, highligh ing a ious inno a i e app oaches and hei impac s on he
assessmen and managemen o seismic isks. By si ua ing his neu al ne wo k
applica ion wi hin i s b oade con ex , he aim is o illus a e i s ele ance and
con ibu ion o ongoing ad ances in seismic enginee ing.
2.3.1 Rela ed wo ks
Neu al ne wo ks and especially Deep Lea ning ha e been in ensely applied in he
ield o seismic enginee ing. This a ea equi es some o he mos complex
s uc u al analysis models because o he nonlinea i y induced by seismic ac ions.
In pa icula , hese nonlinea i ies can be o geome ic ype, e.g.: a s uc u e is
de o med o a poin whe e one can no longe assu e he e icali y o he columns,
hus equi ing ha second-o de e ec s be aken in o accoun . And also,
nonlinea i ies may p esen hemsel es in ma e ial beha iou , e.g.: ein o cemen
s eel wo king pas he elas ic o linea egime in o he plas ic domain. Because o
he impo an challenge ha hese compu a ions pose o ML, many esea che s
ha e eso ed o Deep Lea ning in he ques o p edic he nonlinea beha iou o
s uc u es unde seismic ac ion. Howe e , neu al-based me hods a e no always
he bes choice o he gi en ask. Seismic enginee ing is a b oad ield, and some
p oblems may equi e di e en app oaches.
Fo example, Gong e al. [176] implemen ed an ea hquake-induced damage
iden i ica ion model in buildings using SVM, andom o es , and KNN. In
addi ion, Elwood e al. [177] p oposed an app oach based on uzzy pa e n
ecogni ion o he de ec ion o seismic damage in conc e e s uc u es. Howe e ,
connec ionis models ha e been ex emely powe ul and ha e seen a e y apid
widesp ead adop ion. In his line, Soleimani e al. [178] inco po a e ANN in o
s a e-o - he-a p obabilis ic seismic demand p edic ion me hods o b idge
componen s. Pe ez Rami ez e al. [179] a deep ecu en neu al ne wo k model
based on a nonlinea au o eg essi e exogenous model (NARX) is p esen ed o he
accu a e p edic ion o he seismic esponse o la ge s uc u es. Ruggie i e al. [180]
de eloped an ML amewo k o he ulne abili y analysis o exis ing buildings
based mainly on CNN models o e labelled pho og aphs o hese s uc u es. Won
and Shin [181] de eloped ano he neu al ne wo k-based model ha was able o
apidly p edic seismic esponses wi h soil–s uc u e in e ac ion e ec s and
de e mine he co esponding seismic pe o mance le els. Kwag e al. [182]
36
p oposed a model o p edic he seismic pe o mance o he slope wi h ela i ely
high accu acy and e iciency using ML me hods. They compa e ANN and SVM
me hods wi h a esul much mo e a ou able o he o me . Finally, He e al. [183]
p esen a DL app oach based on a Ga ed Recu en Uni (GRU) ne wo k o assess
he seismic agili y o s uc u es. The GRU ne wo k is used o c ea e a su oga e
model ha cap u es he nonlinea ela ionship be ween seismic esponses and
mainshock-a e shock ea hquakes.
Mo ing on o wo ks ha a e mo e speci ically ela ed o he objec i es o he
case s udy p esen ed in he nex sec ion, a numbe o a icles ha e been iden i ied.
Al hough mos o hem a e based on neu al a chi ec u es, o he ele an me hods
ha e been included which employ o he ML me hods. In [184] ANN we e used
o p edic he s uc u al esponse o di e en loo s o a building o ea hquakes o
a ious in ensi ies. Howe e , hei s udy is limi ed o a modal analysis, whe eas
in he p esen wo k a ull nonlinea s a ic analysis is de eloped. Simila ly, a e y
in-dep h applica ion o neu al ne wo ks was ca ied ou in [185] o p edic seismic-
induced s ess in speci ic elemen s o a wo-span and wo-s o y s uc u e. In con as
wi h he p esen esea ch, hei model is speci ic o a case s udy s uc u e and ained
ne wo ks canno be used o p edic s esses in simila bu di e en s uc u es. This
is also he case o [179], whe e a ecu en neu al ne wo k model wi h Bayesian
aining and mu ual in o ma ion is used o he p edic ion o esponse o la ge
buildings.
Recu en ne s a e a common choice o ime se ies and, mo e b oadly, da a
ha ea u e empo al co ela ions. Al hough no speci ic o esponse p edic ion,
o he wo ks ea u ing ecu en models in he a ea o seismic analysis can also be
ound in he li e a u e [186,187]. In ligh o he esul s ob ained in he case s udy
de eloped o his chap e , he eed- o wa d model a chi ec u e chosen he e was
su icien o add ess he p oblem a hand. Howe e , a ecu en app oach would
pe haps be be e sui ed o he challenges desc ibed in he Fu u e wo k Sec ion
( o ins ance, ex ending he p oposed me hodology o high- ise buildings). Finally,
in [188] a en ion was paid exclusi ely o es ima ing seismic-induced demands on
column splices, and in [189] a mo e gene ic analysis was pe o med, building an
ANN ha p edic s damage in RC shea walls based on he in e -s o y d i .
Howe e , in his case, he d i pe le el mus be calcula ed be o e making use o
he neu al ne wo k.
ANN we e also used as a classi ie o es ablish in which damage-le el ca ego y
a ce ain s uc u e would all in o, o a gi en seismic demand [190,191]. Thei
app oach was he e o e o use neu al ne wo ks o pa e n ecogni ion based on
s uc u al pa ame e s. He e, a mul idimensional eg ession app oach o he
37
applica ion o neu al ne wo ks is used o p edic capaci y cu es, which p o ide a
mo e de ailed beha iou o he s uc u al damage. In he case o [192], a e y
simila app oach o he case s udy in his chap e was adop ed o p edic agili y
cu es wi h neu al ne wo ks. Howe e , since hei s udy was based on dynamic
analysis, capaci y cu es we e no conside ed, in con as o he s a ic app oach
employed in his pape . Fu he mo e, agili y cu es we e no compu ed in a
single un o he ne wo k as p oposed by he p esen me hod. Ins ead, each un
es ima es an indi idual pai o coo dina es, and hen cu es a e e-buil based on
hese es ima ions.
ANN and o he echniques we e also used o p edic he pe o mance poin o
school buildings unde seismic ac ion [193]. Simila ly, in [194] he same objec i e
was aimed ins ead using a gene ic algo i hm, achie ing simila le els o e o . The
ad an age o his las app oach is ha hei model p o ides a anspa en
ma hema ical o mula o he p edic ion o he pe o mance poin . Howe e , hei
s udy ocusses on p edic ing he pe o mance poin di ec ly wi hou conside ing
he capaci y cu es o he buildings.
O he wo ks used neu al ne wo ks o make use o simpli ied app oaches o
de e mine he seismic pe o mance o buildings. In [195], an expe imen al da abase
was used o ain a neu al ne wo k wi h e y ew inpu pa ame e s, se en in o al,
o p edic s ess and de o ma ion alues a speci ic loca ions wi hin
mason y-in illed RC ames unde seismic ac ion. The s udy aims a simpli ying
he complex modelling o mixed-elemen s uc u es bu is s ill limi ed in he scope
o applica ion due o a much- educed numbe o inpu pa ame e s. Finally, in
[196], neu al ne wo ks we e used o p edic a bilinea simpli ica ion o capaci y
cu es wi h accu a e esul s. In con as , in he me hodology ha will be p esen ed
he e, he o iginal capaci y cu es a e p edic ed wi hou simpli ica ion, b oadening
hei scope o applica ion.
2.4. A me hod o en-masse seismic enginee ing analysis wi h
neu al ne wo ks
The objec i e he e is o de elop an accu a e echnique o pe o ming a seismic
assessmen o low- ise buildings by p edic ing hei s ess de o ma ion cu es wi h
ML, employing only a simple se o geome ical pa ame e s o he buildings, a he
han engaging in a edious modelling p ocess.
Today, i is common o use mac o-seismic app oaches o conduc seismic
haza d assessmen [197,198]. In hese me hods, he seismic ac ion is i s
de e mined and hen combined wi h he seismic ulne abili y cu es o he s ock
38
building o calcula e he seismic haza d. Fo example, in Eu ope, i is common o
use he building classes o he RISK-UE p ojec . In con as , when s udying a
building in de ail, a speci ic mechanical model is de ined and calcula ed o i . This
is much mo e accu a e bu equi es many hou s o wo k: he bluep in s o he
building mus be ob ained, he pa ame e s o he ma e ials mus be de e mined, a
model mus be buil by a specialis and, inally, esul s a e ob ained. This is
ob iously oo ime-consuming when calcula ing a la ge numbe o buildings. By
sho cu ing he modelling p ocess wi h ML, his app oach bege s he ad an ages
o bo h wo lds (mechanical and mac o-seismic) while ha ing none o hei
d awbacks. In sho , he main inno a ion and impac is ha i se s a me hodology
o a as en-masse analysis ha p ese es he accu acy o mechanical me hods wi h
negligible loss. In ligh o hese ad an ages, his me hod is se o eplace
mac o-seismic models o seismic haza d assessmen o u ban a eas and eal- ime
seismic e alua ion ools.
P e ious esea ch exis s ha uses ML me hods o p edic s ess/de o ma ion
cu es (o which capaci y cu es can be conside ed a speci ic ype o subse ) o
a ious na u e and di e en con ex s, anging om en i e s uc u es o s uc u al
elemen s and ma e ial s ess es s. Capaci y cu es a e a speci ic ype o s ess /
de o ma ion cu e widely used o pe o m seismic ulne abili y and damage
assessmen s o s uc u es. When calcula ing he capaci y cu es o a building, i
has been shown ha he nonlinea s a ic pusho e me hod yields accu a e esul s,
especially when dealing wi h low- ise buildings ha espond mainly in he i s
ib a ion mode [199].
The me hodology de eloped he e allows o he p edic ion o hese cu es by:
(i) using simple inpu pa ame e s de i ed only om he geome ic and ma e ial
p ope ies o he buildings, (ii) pe o ming in a plas ic egime, (iii) in high
esolu ion o up o 100 poin s pe cu e, (i ) in a single and cohe en p ocess
( a he han a poin -by-poin ashion), ( ) o en i e buildings wi h a g ea ange o
a iabili y in size (limi ed o low- ise), and ( i) wi h immedia e applicabili y o eal
wo ld eme gency elie use cases. These ea u es a e explained in he ollowing
pa ag aphs.
When assessing an indi idual building, his me hod is subs an ially simple
han a ull- ledged nonlinea ime his o y analysis [200]. Howe e , pusho e
analysis is s ill ime-consuming, compu a ionally expensi e and equi es ad anced
modelling expe ise. In gene al, 3D-modelling o s uc u es wi hin enginee ing
so wa e packages is no an op ion when one needs o assess a la ge numbe o
buildings. Fo his eason, he e is an inc easing olume o esea ch ad oca ing he
use o ML echniques ha allow bypassing hese limi a ions. Speci ically, ANN can
39
pe o m nonlinea modelling wi hou p io knowledge o he ela ionships
be ween inpu and ou pu a iables, and consequen ly, i is no su p ise ha many
enginee ing disciplines a e wi nessing an in ense engagemen wi h neu al ne wo k
models o sol e a wide ange o challenging p oblems [201,202,203,204,205].
Seismic analysis equi es accoun ing o s uc u al beha iou in a plas ic egime,
and, o his eason, he p oblem a s ake in ol es highly nonlinea calcula ions. In
mos wo ks, s ess de o ma ion cu es ha e been p edic ed using ML me hods
only in a he cons ained se ings and speci ic samples o s uc u al elemen s. The
p esen app oach conside s no only a ull ange o eal-li e building s uc u es bu
also he modelling o plas ic hinges in s uc u al join s o accoun o he nonlinea
pe o mance o he s uc u al ma e ials (in his case ein o ced conc e e).
Fu he mo e, he model aces a s ong eg ession challenge by p edic ing he
ull capaci y cu e as a se o 100 poin s, which cons i u es a ema kable esolu ion.
In con as o p e ious esea ch whe e each s ess/de o ma ion pai is p edic ed
sepa a ely one by one, he me hodology p oposed he e ackles he ull cu e in one
go, which means ha all he cu e poin s a e deli e ed in a single un o he
ne wo k. This allows o he p edic ion o he ull cu e in a single s ep, bu also o
whe e i s ops. The end poin o he cu e is impo an because i can be indica i e,
o example, o he imminen descen o he s uc u e in o a mechanism leading o
i s o al collapse. These wo aspec s a e missing om p e ious s ess-de o ma ion
p edic ion esea ch, whe eas in he wo k p esen ed he e i is done in a single and
cohe en p ocess.
The choice o ANN esponds, on he one hand, o he ac ha hese models a e
na u ally well sui ed o he challenges ou lined abo e (s ong nonlinea i y and a
la ge eg ession ou pu o up o 100 poin s). And, on he o he hand, i may be
no ed ha Fini e Elemen Me hods (FEM), as used in he SAP2000 calcula ions o
his s udy, aim a sol ing di e en ial unc ions ha a ise om s uc u al analysis.
Neu al ne wo ks, in u n, a e na u ally equipped o deal wi h con inuous and
di e en iable da a ha allow o an e o op imisa ion p ocess h ough he
g adien descen algo i hm. In o he wo ds, he di e en iable cha ac e o he da a
gene a ed by FEM calcula ions is ano he aspec ha makes he p oblem unde
s udy a good i o a neu al ne wo k model. Howe e , wi h ANN, he e is a
well-known d awback in e ms o poo o no explainabili y and he need o
massi e da ase s. Explainabili y is e y impo an in many cases, especially, bu
no only, when dealing wi h human- ela ed da a (medical o li e insu ance a eas,
o example). In he p oblem deal wi h in his pape , a black-box app oach migh
be o gi en in exchange o he e iciency and speed o he model which allows o
as elie o la ge u ban a eas in case o an ea hquake. Wi h ega d o he need o
la ge aining se s, his can be e y p oblema ic when da a is di icul o ob ain.
40
Howe e , his las issue migh be o se by he ac ha he me hodology p oposed
he e allows o he c ea ion o comple e da ase s a will.
As a i s implemen a ion, a ypology o low- ise p isma ic ein o ced conc e e
(RC) buildings has been de ined and a aining se o mo e han 7,000 s uc u es
has been pa ame ically gene a ed. The capaci y cu es o hese models ha e been
ob ained by means o pusho e analysis using SAP2000 so wa e. A e de ining
and aining an app op ia e neu al ne wo k model, ull capaci y cu es a e
p edic ed in a single un o he ne wo k, wi h a esolu ion o up o 100 poin s. This
benchma k is subs an ially highe han p e ious esea ch ha employed less
e icien and comp ehensi e app oaches. The p oblem wi h his common app oach
is no only ha i is slowe , mo e edious, and complica ed, bu also ha he
in o ma ion o whe e he cu e ends is comple ely los .
The me hodology p oposed allows (i) bypassing hea y and highly specialised
compu e calcula ions and complex nonlinea modelling as in [206,207,208], (ii)
allowing as and easy e alua ions in eme gency scena ios as in [209,191,210], and
(iii) p edic ing missing da a as in [192,211,212].
This esea ch is pa o he PERSISTAH p ojec 1, which aims o join ly assess
he seismic ulne abili y o p ima y schools in he Alga e-Huel a egion and
implemen app op ia e e o i solu ions. This egion has been a ec ed by some o
he mos amous ea hquakes in Eu ope (20,21)[213,214]. O 442 school buildings,
mo e han 400 s uc u es in he a ea a e ela i ely simple low- ise RC buildings;
he e o e, hey cons i u e an adequa e objec o he applica ion o he me hod
desc ibed in his pape . This esea ch is also a i s s ep in he SIMRIS p ojec ,
whe e ML echniques a e p oposed o ob ain he capaci y cu es o a la ge da ase
o eal buildings.
2.4.1 Me hodology
Pa ame ic gene a ion o s uc u es
In o de o au oma e he gene a ion o a aining se o he neu al ne wo k, he i s
s ep is o gene a e a la ge numbe o i ual s uc u es, all di e en om each o he
bu alling unde a ypology ha is ep esen a i e o he schools in he Alga e-
Huel a egion. To ca y ou his ask, a se o pa ame e s and alue anges ha e been
chosen based on he lis o school buildings deal wi h in he PERSISTAH p ojec .
These pa ame e s and hei alue anges a e de ined in Table 2.1.
Fo e e y s uc u e, all slabs sha e he same heigh , and he same applies o he
1h ps://keep.eu/p ojec s/21865/P ojec s-o -ea hquaque- es-EN/
41
-SNE [224] and he mo e ecen UMAP [225], which is based on mani old lea ning
echniques and ideas om opological da a analysis. Wi h he UMAP algo i hm,
each o hese ec o s can be mapped in a bidimensional space, so ha all he
samples can be isualised simul aneously as (x,y)poin s in a cha . To ack he
ela ionships be ween he dis ibu ion o hese poin s and some ou pu me ic,
each poin has been colou ed acco ding o he maximum shea o i s co esponding
capaci y cu e. Wi h his colou code, a simpli ied ske ch o how he inpu da a
dis ibu ion aligns wi h i s ou pu can be ob ained as shown in Fig. 2.10. In
pa icula , a ce ain le el o pa e n o ma ion is obse ed, which is desi able o
any ML ask. Howe e , i is also appa en ha hese pa e ns compose a complex
spa ial dis ibu ion which is no i ial o p edic .
Figu e 2.10: UMAP p ojec ion o he inpu da ase . Each sample is colou -coded acco ding o he
maximum shea alue o i s co esponding capaci y cu e.
Cu e da a p e-p ocessing and pos -p ocessing
Some s udies like he ones desc ibed in he p e ious sec ion ha e no a emp ed o
p edic comple e cu es wi hin a single neu al ne wo k a chi ec u e; ins ead, hey
ha e app oached he p oblem by p edic ing indi idual (s ess,displacemen )
48
poin s, hus dis ega ding he p edic ion o whe e he cu e ends. The me hodology
p esen ed he e explo es he possibili y o also p edic ing hese end poin s by
in oducing he comple e cu e as he expec ed ou pu o he ne wo k. This
in ol es he ’p e’ and ’pos -p ocessing’ o he da a poin s ha build up he cu es.
In o de o a ange he da a o each cu e in a way ha can be p ocessed by
he neu al ne wo k, all cu es in bo h he aining and alida ion se s mus be
no malised (Fig. 2.11) and de ined by equal in e als on he displacemen axis and
he same numbe o poin s. The e o e, (i) a esampling o he cu es has been
conduc ed, and (ii) sho e cu es ha e been comple ed wi h a s e ch o cons an
shea alue, as shown in Fig. 2.12.
Figu e 2.11: No malised capaci y cu es o s uc u es #11 (le ) and #34 ( igh ) as e u ned om
SAP2000
Figu e 2.12: Re-sampling o capaci y cu es o s uc u es #11 (le ) and #34 ( igh ) wi h a esolu ion
o 100 poin s and an in e al o 0.01. Cu e poin s o he le o he dashed line co espond o
he o iginal capaci y cu e a e no malisa ion. Cu e poin s o he igh a e included in o de o
comple e sho cu es wi h a s e ch o cons an shea alue.
Once a cu e is p edic ed, i is necessa y o undo his ho izon al s e ch, so ha
he end poin o he p edic ed cu e can be ob ained. Due o he s ochas ic na u e
o he neu al ne wo k used in his s udy, he p edic ion o his ho izon al pa o
he cu e does no yield a pe ec ly s aigh line. Thus, i is necessa y o design an
49
algo i hm capable o cap u ing i , despi e i s i egula i ies. In his wo k, a simple
algo i hm has been designed and implemen ed o his pu pose wi h sa is ac o y
esul s, as ollows: (1) A ole ance alue (adjus ed empi ically o se e he cu es in
he p esen wo k) is es ablished as 1% o he maximum shea alue in he cu e. (2)
Coun he numbe o imes he cu e changes om a nega i e o a posi i e slope
angle o ice e sa ( his has been called a d ibble). (3) Inc ease he ole ance alue
o e e y d ibble occu ence beyond he second one by 0.2% wi h a maximum
possible alue o 5%. (4) I he nex shea alue s ays wi hin he ange o he
p e ious one plus/minus he cu en ole ance alue, hen he poin is lagged as a
po en ial cu e-s op poin and he lagged shea alue is s o ed. (5) I he lag is up,
hen check i he cu en shea alue s ays wi hin he ange o he lagged shea
alue plus/minus he cu en ole ance. (6) I he cu en shea alue s ays wi hin
he a o emen ioned ange, hen coun he numbe o consecu i e occu ences o
his e en . (7) I he end o he cu e is eached while he o me condi ions a e
me , hen e u n he lagged poin i i is a leas he second consecu i e occu ence
calcula ed in he p e ious s ep. (8) I he cu en shea alue lea es he ange
indica ed in S ep 5, hen ese he d ibble coun e , he lagged poin , and he
lagged shea alue. (9) I no condi ion is me a he end o he cu e, hen e u n
he coo dina es o he las poin .
A i icial Neu al Ne wo k
Loss unc ion and e o measu emen s
The ul ima e goal o he neu al ne wo k is o p edic he capaci y cu es o
hose s uc u es s o ed in he alida ion se , gi en he se o simple inpu
pa ame e s associa ed wi h hem, as desc ibed ea lie . To measu e how well his
p edic ion occu s, he ne wo k equi es a loss unc ion which will eed e o alues
in o he op imisa ion p ocess. These alues a e used o adjus he weigh s and
biases o he ne wo k, e ec i ely minimising he e o du ing aining.
The e o e, he loss unc ion es ablishes he me ic agains which he neu al
ne wo k lea ns. In [226] i was indica ed ha he Roo Mean Squa ed E o (RMSE)
and he Mean Absolu e E o (MAE) a e commonly used loss unc ions o he
eg ession o con inuous a iables, i.e. he p oblem unde s udy in he p esen
pape . These loss unc ions a e exp essed as ollows:
RMSE =1/nsn
∑
i=1
(yi−y′
i)2
50
MAE =1/n
n
∑
i=1
|yi−y′
i|
Whe e nis he numbe o neu ons in he ou pu laye , yia e each o he expec ed
ou pu alues, and y′
ia e he co esponding p edic ed alues. This alue will be
calcula ed o each aining sample and backp opaga ed in o he ne wo k o se e
as a c i e ion o weigh op imisa ion. A e in ense aining, he MAE alue will
be as low as possible (and hus he p edic ion e o will be minimum). Bo h e o s
a e simila , bu RMSE penalises la ge e o s mo e se e ely, whe eas MAE p o ides
a linea penalisa ion. In addi ion, RMSE is less in ui i e o in e p e and is sensi i e
o he numbe o samples used o aining. In [227] i is ho oughly analysed and
sugges ed ha e o me ics based on absolu es a he han squa es can pe o m
be e in eg ession p oblems. Fo all hese easons, MAE is chosen o e RMSE.
Because me ics like MAE migh no be e y in ui i e in isual e ms, he esul s
p esen ed he e include h ee o he exp essions o he p edic ion e o , jus o he
sake o cla i y. Fi s , he ull a ea e o % is de ined as he pe cen age a io be ween (i)
he excess a ea enclosed be ween he ue (o es ) capaci y cu e and he p edic ed
cu e, and (ii) he o al a ea delimi ed by he es cu e, as exp essed in Fig. 2.13.
Second, he i ed a ea e o % sha es he same de ini ion as abo e, bu limi ing he
a eas o he lowes o he las displacemen poin s o bo h cu es ( es and p edic ed)
as in Fig. 2.14. Fu he mo e, in he igu es ha ollow, MAE has been exp essed as
a pe cen age o he a ea calcula ed as he sum o all indi idual MAE o each cu e
poin (100 poin s), imes he in e al be ween poin s (0.01).
Figu e 2.13: Full a ea e o scheme (sample #1062)
Thi d and las , he las displacemen e o % e e s o he p edic ion o he end
poin o he cu e and is de ined as he pe cen age a io be ween (i) he absolu e
51
Ld p edic ed
Ld es
Excess a ea
Tes cu e a ea
Figu e 2.14: Fi ed a ea e o and las displacemen (Ld) e o schemes (sample #1062)
di e ence be ween he p edic ed and ue end poin s o he cu e and (ii) he ue
end poin , as shown in Fig. 2.14.
These measu emen s, especially he i ed a ea e o % and he las displacemen
e o %, allow o he sepa a e e alua ion o (i) how well he cu es i each o he in
e ms o shape and (ii) how well he ne wo k has p edic ed he end o he cu e.
Ne wo k a chi ec u e
The i s a emp o de ine a ne wo k a chi ec u e is o implemen a s anda d
eed- o wa d model. Because he e is no heo e ical me hodology o es ablish he
op imal con igu a ion o he ne wo k [228], a s epped p ocess, ha is, a g id sea ch,
has been designed o de e mine he mos app op ia e a chi ec u e o he neu al
ne wo k model. Mo e ho ough me hods such as op imising he a chi ec u e wi h
gene ic algo i hms [229,230] can be explo ed in u u e wo k. In a i s phase, a single
laye ne wo k is se up wi h a ying sizes o he hidden laye : (a) a hidden laye
equal o he size o he inpu , (b) equal o he ou pu laye , (c) a alue in be ween,
and (d) la ge han he ou pu laye , as seen in Fig. 2.15. This helps in assessing
wha ange o sizes in he hidden laye sui s he p oblem bes .
Wi h his in o ma ion a hand, ano he se o a chi ec u es o a ying dep h (i.e.
a a ying numbe o hidden laye s) is e alua ed. These laye s use he p e ious size
alue as an ini ial o en a i e laye size. I mus be men ioned hough, ha his
alue is used only empo a ily since mo e adjus men s on he sizes o he hidden
laye s will be ca ied ou la e in he p ocess.
Deep neu al a chi ec u es can be ex emely powe ul. When applied o
eg essions o con inuous a iables and ime se ies (simila o he examples in his
s udy), hese models show a g ea pe o mance [231,232,233]. Howe e , he e is a
52
Figu e 2.15: Va ying hidden laye sizes, ( op le ) h1=30, ( op igh ) h1=65, (bo om le ) h1=100,
(bo om igh ) h1=135
ade-o be ween he complexi y ha a neu al ne wo k can b ing o wa d and he
o e i ing o he model o he da a. Due o o e i ing, deep a chi ec u es may
pe o m e y well on he aining samples bu poo ly on he alida ion da a. To
es he in e play o hese ac o s, h ee ini ial a chi ec u es a e p esen ed p ima ily
acco ding o he numbe o hidden laye s (dep h). In he ollowing, Fig. 2.16 shows
a diag am o hese schemes.
Figu e 2.16: Va ying dep hs in ne wo k a chi ec u e, 2 (le ) and 3 ( igh ) hidden laye s.
In bo h Figs. 2.15,2.16,x ep esen s he inpu neu ons o he ne wo k. As seen
in p e ious sec ions, he o al numbe o inpu s o he ne wo k is ixed o 30 as his
ma ches he numbe o pa ame e s ha ha e been used o gene a e he buildings.
The e o e, h ep esen s he hidden laye s in he model. An ini ial size is
empo a ily se a 65 as i is he bes pe o ming size in a p elimina y and in ui i e
e alua ion, bu mo e e ined alues will be explo ed la e . Finally, yis he ou pu
53
laye , which co esponds o he alues o he capaci y cu es ha he ne wo k is
aiming o p edic . The size o his ou pu laye has a s ong impac on he
pe o mance o he lea ning p ocess. Small sizes in his laye educe he le el o
di icul y o he p edic ions; howe e , a alid esolu ion o he cu es mus be
ensu ed. Fo his eason, he numbe o neu ons in he ou pu laye has been
ini ially se a 100 because i p o ides enough esolu ion o g aph he capaci y
cu e as discussed and i is sligh ly highe han he maximum numbe o poin s
p esen in he o iginal capaci y cu es as e ie ed om SAP2000. Howe e ,
a ia ions in his ou pu size will also be discussed la e .
F om his ou se , he main algo i hms o he ne wo k will be explo ed, namely
he ac i a ion unc ions ha a e implemen ed in each laye (which may be
conside ed an algo i hm when iewed as a whole) and he e o op imisa ion
algo i hm.
Ac i a ion unc ion
Neu al ne wo ks a e e y sensi i e o his elec ion, and he e a e many possible
ac i a ion unc ions used in neu al ne wo ks, so i mus be de e mined which one
i s he p oblem bes . In [234] i was obse ed ha a Hype bolic Tangen (Tanh) is a
common ac i a ion unc ion applied o he hidden laye s o a neu al ne wo k o
simila p oblems as he one discussed in his s udy, while sigmoid ac i a ions a e
commonly used o he ou pu laye (as hey map om 0 o 1). Fo his eason, bo h
Tanh and sigmoid ac i a ion unc ions will be es ed in hidden and ou pu laye s,
espec i ely. Al e na i ely, in a ine- uning phase, Rec i ied Linea Uni (ReLU)
ac i a ion has also been es ed due o i s common use in deep neu al a chi ec u es
[235] bu wi h no posi i e esul s.
Op imise
A p elimina y choice o he op imisa ion algo i hm is S ochas ic G adien
Descen (SGD), which is he basic algo i hm o neu al ne wo k aining [236].
Ne e heless, in a la e s age, a second algo i hm has been es ed, namely he
Adadel a op imise [237], which is a a ian o he SGD ha p esen s a no el
lea ning a e me hod pe dimension o g adien descen by dynamically adap ing
o e ime. The applica ion o his op imisa ion algo i hm did no imp o e he e o
a e ob ained using SGD.
P elimina y adjus men o SGD pa ame e s
As explained in he me hodology sec ion, he i s objec i e is o ix he
a chi ec u e o he ne wo k and he pa ame e s o he op imise algo i hm. In o de
o es a ious a chi ec u es eliably, a sa is ac o y se o pa ame e s is equi ed o
54
guide he backp opaga ion o he e o . Fo his pu pose, a simple ini ial
a chi ec u e is de ined.
The ini ial condi ions o he p elimina y adjus men o SGD a e shown in Table
2.3. SGD is adjus ed h ough he ollowing pa ame e s: Lea ning a e (L ), Decay,
and Momen um (M). The esul s a e measu ed agains he alida ion se using MAE
(Table 2.4 and Fig. 2.17).
Ne wo k A chi ec u e
Laye s X h1 Y
Laye size 30 65 100
Ne wo k Pa ame e s
Laye s X h1 Y
Ac i a ion - Tanh (Hype bolic Tangen ) Sigmoid
Weigh ini ialisa ion - Random seed wi h ange (0, 0.1) Random seed wi h ange (0, 0.1)
Bias ini ialisa ion - Random seed wi h ange (0, 0.1) Random seed wi h ange (0, 0.1)
T aining Pa ame e s
Epochs(ep) 200
Ba ch size 12
Shu le samples
a each epoch Yes
Table 2.3: Ini ial condi ions o p elimina y S ochas ic G adien Descen (SGD) adjus men .
L (Lea ning a e) Decay M (Momen um)
MAE loss MAE loss MAE loss
0.15 0.0159 L /800 0.0158 0.80 0.0160
0.20 0.0157 L /1000 0.0156 0.85 0.0156
0.25 0.0156 L /1200 0.0155 0.90 0.0150
0.30 0.0156 L /1400 0.0154 0.95 0.0181
0.35 0.0154 L /1600 0.0150 Nes e o 0.0149
0.40 0.0157 L /1800 0.0152
0.45 0.0159 L /2000 0.0154
Fixed pa ame e s
Decay = L /1000 L = 0.35 L = 0.35
M = 0.9 M = 0.9 Decay = L /1600
Table 2.4: Expe imen a ion and esul s o p elimina y SGD adjus men .
Ne wo k a chi ec u e con igu a ion
Once he op imisa ion pa ame e s ha e been se , i is hen possible o es
di e en ne wo k a chi ec u es mo e e ec i ely. In hese es s, Tanh ac i a ion in
he hidden laye s and sigmoid ac i a ion in he ou pu laye a e ixed.
55
Figu e 2.17: Loss/Epochs g aph wi h selec ed SGD alues o p elimina y adjus men .
In Table 2.5, he ini ial condi ions o he a ia ions in ne wo k a chi ec u e a e
shown. Then Table 2.6, Figs. 2.18–2.20 p esen he es s and esul s o he ne wo k
a chi ec u e showing di e en a ia ions o e hidden laye s. In Table 2.7, he esul s
o he cu e esolu ion (size o he ou pu laye ) a e lis ed.
Figu e 2.18: Valida ion loss/Epochs g aph o 30-205-100 laye scheme (1 hidden laye )
Ne wo k pa ame e ine- uning
A e ob aining he bes e o a es o all he con igu a ions es ed, a inal
a chi ec u e 30-65-65-100 is selec ed. F om his se up, a mo e e ined se o
a ia ions is execu ed. These a ia ions include a second ound o SGD op imise
pa ame e s, as well as an a emp on he Adadel a op imize , ReLu ac i a ion o
hidden laye s, and di e en ba ch sizes. The numbe o aining epochs is always
p olonged un il he e o does no imp o e signi ican ly.
56
Ne wo k Pa ame e s
Laye s X h1 Y
Ac i a ion - Tanh (Hype bolic Tangen ) Sigmoid
Weigh ini ialisa ion - Random seed wi h ange (0, 0.1) Random seed wi h ange (0, 0.1)
Bias ini ialisa ion - Random seed wi h ange (0, 1) Random seed wi h ange (0, 1)
T aining Pa ame e s
L (Lea ning a e) 0.35
Decay L /(8.ep)
M (Momen um) Nes e o
Epochs (ep) 800-1200
Ba ch size 12
Shu le samples Yes
Table 2.5: Ini ial condi ions o ne wo k a chi ec u e a ia ions.
Laye scheme & size MAE loss
X h1 Y Valida ion e o T aining e o
30 30 100 0.0153
30 65 100 0.0135
30 100 100 0.0132
30 135 100 0.0131 0.0115
30 170 100 0.0132
30 205 100 0.0133
Laye scheme & size MAE loss
X h1 h2 Y Valida ion e o T aining e o
30 30 30 100 0.0133
30 30 65 100 0.0137
30 30 100 100 0.0137
30 55 80 100 0.0128
30 65 65 100 0.0126 0.0106
30 65 100 100 0.0131
30 100 100 100 0.0134
Laye scheme & size MAE loss
X h1 h2 h3 Y Valida ion e o T aining e o
30 30 30 30 100 0.0137
30 30 30 65 100 0.0133 0.0107
30 30 65 65 100 0.0138
30 65 65 65 100 0.1407
Table 2.6: Resul s o hidden laye /s a chi ec u e.
57
Figu e 2.28: Fi ed a ea e o ˜ 5.0%. Valida ion sample #147.
Figu e 2.29: Ld <5.0%. Valida ion sample #639.
Figu e 2.30: Ld ˜ 21.32%. Valida ion sample #1971.
2.5. Discussion
Following he me hodology desc ibed in he p e ious Sec ion, ini ial es s we e
ca ied ou o ind an op imal alue o he SGD pa ame e s o he ne wo k. The
64
Figu e 2.31: Ld ˜ 60.0%. Valida ion sample #1926.
esul s ha e e ealed ha wi h a simple ini ial a chi ec u e (30-65-100) he ne wo k
is capable o high p edic ion accu acy.
The es s on di e en ne wo k a chi ec u es yielded he bes esul s o
con igu a ions ha ea u ed wo hidden laye s; in pa icula , he scheme ha
deli e ed he bes esul s was 30-65-65-100. A chi ec u es wi h only one hidden
laye e u ned be e esul s wi h la ge sizes, bu s ill no as compe i i e as he
la e . The ac ha he ne wo k clea ly pe o ms be e when inc easing i s
complexi y accoun s o he le el o di icul y o he p edic ions. Howe e , a e a
ce ain poin , inc easing he complexi y o he model does no imp o e he esul s
due o o e i ing. Pe haps, wi h an e en la ge aining se , hese deepe
a chi ec u es may imp o e he esul s, hus lea ing oom o u u e wo k.
Rega ding he size o he ou pu laye , and a he coun e -in ui i ely, smalle
sizes o cu e esolu ion ha e no imp o ed he me ics. An ini ial ou pu laye size
o 100 was se because i was conside ed o ha e enough esolu ion o he p oblem
a hand while no being excessi ely la ge o aining. In e es ingly, lowe ing his
alue p o ed de imen al while e en ually inc easing i s size o 135 yielded equally
accu a e esul s. This can be explained by he ac ha lowe esolu ions a e less
loyal o he calcula ion algo i hms wi hin he enginee ing so wa e which p oduced
he alida ion se o capaci y cu es (SAP2000), and since neu al ne wo ks pe o m
bes wi h clea pa e ns, lowe esolu ions in oduce ha m ul noise in he aining
p ocess.
Finally, in he ine- uning s age, ba ch sizes played an impo an ole in
maximising he cu e p edic ion accu acy. Al hough he e may be some
disag eemen abou he egula ising e ec o ba ch size [239,240], in hese
expe imen s i was ound ha la ge ba ch sizes can p e en o e i ing by
egula ising he ne wo k o some ex en , because loss alues a e a e aged o all
65
he elemen s in he ba ch and hen backp opaga ed o adjus he weigh s and biases
o he model. Table 9 shows how he lowes ba ch sizes had e y good aining
esul s, bu lagged when es ed agains he alida ion se , hus showing a mo e
acu e o e i ing. The bes pe o ming ba ch size es ed was 24 samples.
In he me hodology p esen ed, no modelling o he speci ic building is equi ed.
Cu es can be es ima ed wi h an a e age cu e-a ea i ing abo e 97.6%, equi ing
only he basic geome ic pa ame e s o he building o be speci ied.
The main conclusions o his s udy can be summa ised as ollows:
• ANN p o ide an accu a e app oxima ion me hod o he nonlinea s a ic
pusho e calcula ion o low- ise s uc u es wi hin a wide ange o sizes and
geome ic con igu a ions.
• The accu acy o he me hod success ully add esses he sho comings o cu en
mac oseismic app oaches while emaining as and e icien .
• S ess-de o ma ion cu es in a plas ic egime can be p edic ed wi h ANN in
one go o en i e buildings using only basic geome ic pa ame e s. Fo low- ise
s uc u es, his wo k achie es a cu e a ea e o below 2.7% and a esolu ion
o up o 100 poin s.
• The ela i e simplici y o he ANN a chi ec u e equi ed o p edic he capaci y
cu es o low- ise buildings makes a s ong case o u u e esea ch o high-
ise s uc u es using deepe ne wo ks and la ge da ase s.
In u u e wo k, i may be in e es ing o include he use o gene ic algo i hms o
e ol e an e en mo e op imal ne wo k a chi ec u e. Fu he mo e, a compa ison wi h
o he eg ession me hods o ML app oaches would be desi able o con ex ualise he
esul s ob ained.
In he long e m, i migh be in e es ing o explo e a simila app oach wi h
dynamic analysis, high- ise buildings wi h highe ib a ion modes, and a wide
a ia ion o sec ional and ma e ial p ope ies. I should also be no ed ha his
wo k has ollowed he Eu ocode-08 capaci y spec um me hod, which has been
p o en o wo k well wi h low- ise s uc u es. Howe e , a esea ch e o o p edic
capaci y cu es unde a se o s ong ea hquakes ha can p oduce g ea e
nonlinea i ies would ex end he applicabili y o he me hod p esen ed he e. All
hese cases (dynamic analysis, high- ise buildings, and s onge ea hquakes) pose
a g ea e challenge in e ms o ML and may equi e he use o mo e specialised
neu al ne wo k a chi ec u es. In his ega d, because capaci y cu es can be
ega ded as ime-dependen se ies, ne wo k models be e sui ed o handle
dynamic inpu , such as ecu en neu al ne wo ks [241,242], should be explo ed.
66
3. Applica ion o gene a i e A i icial In elligence o
seismic esilience: Au oma ed ex ac ion o building
ypologies om digi al u ban cadas e s
This chap e is mean o be a ansi ion om enginee ing applica ions o neu al
ne wo ks o he wo ld o neu al models o gene a i e AI. I is s uc u ed as a case
s udy ha builds on he wo k p esen ed in he p e ious chap e . In pa icula , in
he ollowing sec ions, a me hod is p oposed o ex ac building ypologies om a
digi al land cadas e. In doing so, he in en ion is o expand he s udy on seismic
demand p edic ion o he mos ele an ypologies o any gi en ci y. Thus,
al hough his chap e can be seen as a con inua ion o he p e ious one on seismic
enginee ing, i shows a mo e unc ional angle (u ili as) on an u ban scale. A he
same ime, i in oduces an example o he VAE model ha will be explo ed in
g ea e dep h in he nex chap e . The VAE model ha will be used he e a ge s
image-based inpu s o building oo -p in s, which se es as an in oduc o y case
s udy o he mo e challenging h ee-dimensional p oblem p esen ed la e .
3.1. In oduc ion and li e a u e e iew
Recen ad ances in Machine Lea ning echniques a e ha ing a g ea impac on he
ield o mac oseismic analysis. Un il no so long ago, he e used o be a ade-o
be ween he le el o de ail o he analyses and hei easibili y, pa icula ly in e ms
o cos , ime consump ion and man powe . The e o e, mac oseismic s udies
de o ed many e o s o inding e ec i e s a egies o he deli e y o accep able
app oxima ions o he assessmen o la ge u ban a eas, employing a easonable
amoun o ime and esou ces. Howe e , his s a us quo is being ans o med a a
e y apid pace wi h he de elopmen o ML applica ions o hese mac oseismic
challenges. The p e ious chap e [243] p esen ed an a i icial neu al ne wo k ha
was ained o p edic he capaci y cu es o p isma ic ein o ced conc e e (RC)
buildings o up o ou s o ies and spanning a e y wide ange o loo plan
dimensions. The p esen ed neu al ne wo k model can ou pu capaci y cu es om
only basic geome ic pa ame e s, such as he numbe o spans in he X,Yand Z
axes and he ea u es o he beams and columns in he s uc u e. As a consequence,
eme gency elie agencies can assess he seismic ulne abili y o la ge numbe s o
buildings e y quickly wi hou engaging in edious s uc u al modelling.
The wo k p esen ed now is pa o a la ge e o in expanding hese
67
de elopmen s o accoun no only o p isma ic buildings, bu o he majo
building ypes p esen in a gi en u ban a ea. Recen wo k add essing he same
objec i es can be ound, o example, in [244]. Howe e , he app oach he e
a emp s o achie e en-masse seismic analysis a he le el o indi idual building
modelling. A i s s ep in his di ec ion en ails iden i ying hese ypes in an e icien
way, which is he main objec i e o his case s udy. Fo he as majo i y o
buildings, he s udy o hei ypology can be add essed solely om he shape o
hei loo plan bounda y o pe ime e , also commonly e e ed o as ‘ oo -p in ’.
This is an impo an ad an age, mainly due o he ac ha oo -p in s a e ypically
a ailable as pa o a ci y’s geog aphic in o ma ion sys em (GIS). Fo his case
s udy, mo e han 100k o hese shapes ha e been collec ed om he digi al land
cadas e o Se ille (Spain) in o a da abase bo h in ec o and as e (pixel) o ma .
The challenge, as men ioned ea lie , is o ex ac o clus e hese oo -p in shapes
in o cohe en ypes ha a e ep esen a i e o pa ame ically simila s uc u al
de ini ions. This will allow he c ea ion o la ge da abases o building s uc u es o
ain ANN models, as desc ibed in [244].
Shape Clus e ing is a well-de eloped ield o esea ch wi h impo an
con ibu ions da ing back, a leas , o he 1970’s (wi h e en ea lie s udies by Si
D’A cy Wen wo h Thompson in 1917). Kendall de ined shape as he geome ic
in o ma ion ha emains a e il e ing ou loca ion, scale and o a ion [245]. Then
in [246], P oc us ean analysis (coined by Hu ley & Ca ell in 1962 [247]) was
in oduced o he analysis o shapes, and consolida ed in “P oc us es Me hods o
he S a is ical Analysis o Shape” [248]. The P oc us es me hod in ol es inding he
op imal ansla ion, scaling and o a ion o a shape wi h espec o a e e ence
shape. The objec i e is o minimise some e o , o dis ance, es ablished among he
wo se s o landma k poin s o each shape. Landma k poin s in u n a e de ined as
ep esen a i e poin s wi hin he shapes ha ma ch ac oss he popula ion o shapes
unde s udy.
Mo e wo ks ollowing his ini ial phase we e ca ied ou in he ea ly 2000s [249,
250]. Then, a mo e gene al and powe ul me hod was p oposed by [251], which was
able o emo e he need o landma k-based shapes and compu e shapes in he o m
o ull con inuous cu es. These achie emen s we e u he consolida ed by o he
wo ks such as [252,253]. Ano he impo an de elopmen was b ough abou by he
wo k o Ama al e al. [254]. In hei con ibu ion “k-Means Algo i hm in S a is ical
Shape Analysis”, he au ho s opened he doo o he s udy o shape clus e ing using
s anda d clus e ing algo i hms. Howe e , as in all p e ious s udies, he esul o
hese compu a ions elied hea ily on he e o o shape dis ance selec ed. In [255],
se e al me ics and app op ia e clus e ing me hods a e e alua ed o a se o wo-
dimensional shapes ha include Euclidean and non-Euclidean me ics such as he
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Riemannian dis ance. Finally, some wo ks ha e a ge ed he applica ion o hese
shape clus e ing me hods o he ields o A chi ec u e and Design [256,257,258,
259].
Shape clus e ing as pe he cu en s a e-o - he-a elies on p io knowledge o
he shape space. Fo example, i needs he numbe o clus e s o be speci ied
be o ehand, and, mo e impo an ly, he e has o be a p ocess o ei he de i e he
e e ence shape o each ca ego y o a e e ence shape has o be di ec ly p o ided
al oge he o each ca ego y so ha he dis ances o e o me ics can be es ablished
upon. The e o e, unsupe ised exe cises a e pe haps be e sui ed o di e en
clus e ing echniques and app oaches. Fo his eason, a Va ia ional Au oencode
(VAE) [260] model is es ed o he pu pose o ex ac ing ypologies om a land
cadas e. This app oach is also use ul o il e ing ou ypologies ha a e no
ep esen a i e o do no appea in su icien numbe s wi hin an u ban con ex . This
is a na u al e ec ha de i es om he aining aspec s o neu al ne wo ks, whe e
less equen samples in a aining da ase a e ’igno ed’ by he model. Clus e ing
wi h VAEs has wi nessed a s ong inc ease in con ibu ions om he li e a u e in
ecen yea s [261,262], including he use o con olu ional a chi ec u es o image
clus e ing [263], as is he scope o his case s udy. While he a o emen ioned s udies
ocus on benchma king agains well-known da ase s (achie ing imp essi e
esul s), he e he objec i e is o es a s aigh o wa d model on a eal-wo ld
p oblem, and i is expec ed ha he applica ion-speci ic po en ial and alidi y o
he me hod may be assessed in he con ex o building ype analysis wi hin la ge
u ban a eas.
3.2. Me hodology
The basic p emise o he me hod is he use o a VAE o pe o m unsupe ised
clus e ing o images. A la ge se o p e-p ocessed oo -p in image samples is ed o
he model o aining. Once he VAE is ained, he la en space is app oxima ed
by a Gaussian dis ibu ion. Sampling om his space, a se o econs uc ed images
p o ide a summa y o he building ypologies in he o iginal da ase (see Fig. 3.1).
All o hese s eps a e explained in de ail h oughou his sec ion.
The shapes s udied a e aken om he o icial land cadas e o he ci y o Se ille
in Spain, which is a ailable as a ec o -based ESRI shape ile. The ile con ains he
oo -p in s o all he buildings and o he buil en i ies in he municipali y o Se ille,
o alling mo e han 100k eco ds. These ou lines a e in he o m o closed polylines
and a e p o ided wi h a se o da a ields indica ing he numbe o loo s, he da e
o en y in he da abase, he su ace a ea and o he in o ma ion. On a p elimina y
isual explo a ion, he ollowing obse a ions a e made:
69
Figu e 3.1: G aphic summa y o he me hodology.
• Polylines p esen an a bi a y numbe o e ices ( o example, a mo e o less
pe ec ec angle may ha e a lo mo e han ou poin s).
• The ou lines co espond no only o buildings bu also o o he u ban
s uc u es such as e en ion walls, unde g ound and su ace pa king e c.
• The d a ing quali y o he ou lines is a he de icien in many cases, whe eby
polylines o en o m sha p spikes ha do no seem o co espond o he ac ual
buil objec s.
• Many buildings ha a e known o be o hogonal p esen some angle
dis o ions ha al hough no exagge a ed, can s ill be iden i ied as
non-o hogonal in a quick isual check.
To coun e hese issues, a numbe o p ep ocessing p ocedu es a e employed.
3.2.1 P e-p ocessing
Because he numbe o poin s will be used u he in he me hod o c ea e di e en
da ase s, he i s simpli ica ion p ocedu e will a emp o elimina e i ele an
polyline poin s. The c i e ion is o elimina e a e ex ha joins wo segmen s wi h
an angle smalle han a h eshold alue (see Fig.3.2). This h eshold alue (<π/40)
has been adjus ed so ha cu ed building ou lines a e no a ec ed.
The second p e-p ocessing s ep aims o iden i y and emo e sha p spikes ha
esul om ‘sloppy’ d a ing. In his case, he s a egy adop ed has been wo- old:
i s , sha p angles (below a chosen h eshold: <π/8) a e lagged, and hen hose
lagged angles belonging o sho polyline segmen s (a second h eshold is se he e:
<1m) a e emo ed (see Fig. 3.2).
Thi d, since he shapes unde s udy should co espond o building ypologies,
70
en i ies ha a e clea ly nei he buildings no ep esen a i e buildings a e il e ed
ou . To his ca ego y belong (i) e y la ge (>900m2) o small (<100m2) en i ies, (ii)
hose ha do no span a single loo in heigh , and inally, (iii) linea -like en i ies,
de ined as a minimum h eshold a io be ween hei su ace and pe ime e leng h.
Figu e 3.2: P e-p ocessing s eps #1 and #2: emo al o sha p spikes and edundan e ices.
Addi ionally, u he p e-p ocessing is ca ied ou o add ess po en ial issues
du ing he lea ning p ocess o he VAE model. The dominan issue is ha a VAE
model can lea n he dis ibu ions o posi ion, size, and o a ions ac oss he
samples, as discussed in he p e ious chap e [264]. Thus, simila ly o he
P oc us es idea desc ibed ea lie , all samples a e ansla ed o he same posi ion in
space (0, 0)and scaled (isomo phic) o he same bounding-box size. Ro a ions,
howe e , pose a g ea e challenge, because i is no possible o de e mine a
e e ence o a ion o any o he shapes wi hou a p io hea y-du y s udy. Hinging
on he design a ionali y o he as majo i y o he building s ock o a ci y, a ou h
p e-p ocessing s a egy ha iden i ies he p incipal ec o di ec ions o each
building ou line is p oposed. In his app oach, all segmen s o he ou line polyline
a e clus e ed using a e e ence angle (<π/20), which means ha in each clus e ,
any gi en pai o segmen s p esen an angle lowe han he chosen h eshold. The
a e age angles o di ec ions o he clus e s ha ha e he longes agg ega e segmen
leng h (sum o he leng hs o each segmen in he clus e ) become he p incipal
di ec ions. I is acknowledged ha PCA (P incipal Componen Analysis) migh be
a mo e sui able app oach o sol e his p oblem. An example o p incipal di ec ions
is illus a ed in Fig. 3.3. Finally, each shape is o a ed o align he op-mos
p incipal di ec ion o he Xaxis. O cou se, his me hod does no gua an ee ha
same- o-be shapes may no p esen a 90º, 180º o 270º wi h espec o each o he ,
bu i does educe he o a ion di e ences ha migh be lea n by he VAE o only
hose h ee op ions.
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Figu e 3.3: P e-p ocessing s ep #4: o a ion along op-mos p incipal di ec ion and isualisa ion o
p incipal di ec ions.
3.2.2 Gene a ion and augmen a ion o aining and alida ion se s
Fo he gene a ion o he da ase s, all he p ep ocessed ec o ou lines a e
con e ed in o solid image-based shapes (black-colou ed wi h g eyscale an ialias
bo de s). Fo buildings wi h pa ios, he pa io is colou ed in he same colou as he
backg ound (whi e). The main eason being ha VAE models and in gene al neu al
ne wo ks a e e y e icien a wo king wi h pixel-based da a such as images.
Because he e a e po en ially qui e a numbe o di e en building ypes wi hin he
da ase , he challenge o he model is a he huge. Fo his eason, and despi e he
al eady la ge numbe o samples a ailable, a da a augmen a ion scheme has been
implemen ed: each sample is andomly o a ed wi hin a small angle ange
(±π/50) and also displaced andomly wi hin a ma ginal ange (±2.5% o he
wid h and heigh o he image o Xand Y espec i ely). Wi h his app oach,
depic ed in Fig. 3.4, i is possible o augmen he da ase mo e han 100- old. Two
comple e da ase s (be o e spli ing in o aining and alida ion) we e gene a ed o
expe imen a ion: a ’ la ’ da ase (se A) whe e each sample was andomly o a ed
and ansla ed 100 imes, inc easing he a ailable da a 100- old, and also a
’p og essi e’ da ase (se B), whe e he numbe o ins ances andomly gene a ed
om each shape was p opo ional o i s numbe o landma k e ices
(numbe o ins ances =100 ∗(n+ (n−4)), whe e nis he numbe o e ices). The
in en behind his idea is o allow mo e complex building ypes (assuming simple
shapes a e o e - ep esen ed) o inc ease hei ela i e ep esen a ion in he inal
da ase . In essence, he s a egy de ised o he p og essi e da ase aims o
alle ia e he well-known class imbalance p oblem [265]. Bo h da ase s ea u e a
numbe o samples abo e 1.5M and a e spli 70 / 30 in o aining and alida ion
se s, espec i ely.
3.2.3 Va ia ional Au oencode model
Finding he op imal neu al model o a gi en da ase and loss unc ion is a
non- i ial ask. In ac , he e is no o mal me hod o de e mine an op imal
72
Figu e 3.4: Da ase augmen a ion h ough andom o a ions and displacemen s.
a chi ec u e o deep lea ning models [228]. Mo e so, in he case o VAEs, as hei
loss unc ion includes no only he econs uc ion e o bu also he
Kullback-Leible (KL) di e gence [266] be ween he a ge and he ob ained la en
space dis ibu ions. Howe e , he e a e me hods ha help o ind a sui able model
con igu a ion, such as Gene ic Algo i hms [229,230]. These me hods would
in ol e e y hea y compu a ion powe o he da ase a hand (beyond a egula
pa allel compu ing pla o m such as he CUDA engine – which has been u ilised in
he expe imen a ion). They also equi e cu ing-edge expe ise in deep lea ning.
The aim o his wo k is o p o e ha he me hod is sui able o he p oblem a
hand, a he le el o a p oo -o -concep , and no o ind an op imal pe o mance o
he model. In ligh o his con ex , many o he ne wo k con igu a ion se ings a e
d awn om p e ious esea ch [264].
The expe imen a ion is conduc ed in wo phases: a p elimina y explo a ion
and a ull-scale s udy. The objec i e o he p elimina y explo a ion is o acqui e a
‘ eel’ o he model. In his phase, a educed da ase is used o abou 150k samples,
which is 10% o he inal da ase used. The educ ion is achie ed simply by limi ing
he gene a ion o andom samples om 100× o 10×, so ha he di e si y o
building ypes emains cons an . The ange o a chi ec u e de ini ions o he VAE
models designed o his p elimina y phase is p esen ed in Fig. 3.5, om he i s
and simples i e a ion (a) o he bes pe o ming (b). This se ies o models ea u es
wo 2D con olu ion laye s o a ying dep h and con olu ion ma ix size. The i s
is applied o e he inpu laye ha is 60×60 in size ac oss all expe imen s. The size
o he second one is exac ly hal (30×30) o a hi d (20×20), and he ansi ion om
one o he o he is p ocessed by a down-sampling laye . The me hod selec ed o
he educ ion in size is a e aging ( he alue o each neu on in he a ge laye is
compu ed as he a e age o he co esponding alues o he sou ce laye ). A he
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shape may no add much mo e aluable in o ma ion o he models. Thus, om a
me hodological pe spec i e, i seems as hough he da a augmen a ion ac o used
o phase 1 is wi hin a be e magni ude ange o he p oblem a s ake han he
size implemen ed in phase 2. Fo his eason, no es s ha e been conduc ed o he
ull p og essi e da ase (se B) and he inal shape ex ac ion esul s ha e been
aken exclusi ely om phase 1.
Wi h ega d o he ex ac ion o building ypologies, a o al o 24 o 26 di e en
ypes ha e been ex ac ed depending on c i e ia (Fig. 3.9). Mos o hem a e sou ced
om he p og essi e da ase , as i pe o med be e in e ms o loss minimisa ion
and also deli e ed he b oades a ie y o shapes (Fig. 3.10). O cou se, he e is a
subs an ial o e lap be ween bo h se s; hus some o he ypes in Fig. 3.9(up) can
also be ex ac ed om he la da ase (se A). The e o e, Fig. 3.9(down) shows only
hose ypes ha a e no ex ac ed o a e no e y clea om he se B. Fo example,
D3 co esponds o a e y common ypology commonly e e ed o as ‘H-block’ bu
is no clea ly depic ed. Howe e , E6 po ays a much mo e accu a e ep esen a ion
o his ypology. A simila case occu s be ween A6 and E2, al hough in his case he
di e ence is ba ely isible ( he la e is a bi clea e han he o me ). This ype also
co esponds o a e y common building ha is ound in he old qua e o he ci y
cen e o Se ille. I ea u es a small pa io on he back, while he ac¸ade a icula es a
buil -in body ha hos s a se o glazed balconies along each s o ey. Then, E3 (ci cula
o ound buildings), E4 (L-block) and E5 (cham e ed L-block) ha e been ex ac ed
only om he se A(no p esen a e sampling om PH1 B2). Finally, E1 (open
C-block) could a guably be classi ied in he same ca ego y as C4. In such cases, i is
di icul o es ablish clea c i e ia o when o d aw he line be ween wo ca ego ies.
In ac , i may be a gued u he ha C6 should belong o his ca ego y as well,
and ha he dis inc ion be ween a C-block and an open C-block is a he weak and
unsubs an ia ed. A simila si ua ion also occu s be ween B1 and D4. In eali y,
hese ypes o building co espond o e y di e en a chi ec u al con igu a ions.
Thus, i may be sugges ed ha he capaci y o he model o p o ide his le el o
di e en ia ion ep esen s an impo an (and un o eseen) s eng h o he me hod.
O e all, he models ha e cap u ed he mos well-known building ypes, and
also many o he s ha would ha e equi ed long manual supe ision o iden i y
(such as A1, B6, C1, and B2). Fu he mo e, he me hod has il e ed ou many a e o
uncommon ypologies ha a e no ep esen a i e o he u ban ab ic ( o example,
he buildings in Fig. 3.3). I is also e y possible ha he me hod has no been able o
iden i y some ele an building ypes. Finally, i is e y impo an o no e ha VAE
a e essen ially gene a i e. This means ha hey a e able o c ea e new shapes by
in e pola ing wo o mo e exis ing ones. In ela ion o he ma e o his case s udy,
i implies ha some o he building ypes ex ac ed and p esen ed in Fig. 3.9 migh in
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ac be en i ely ic ional. In gene al, i is expec ed ha hese in e pola ions p esen
a less de ined image p o ile han hei non- ic ional coun e pa s. Howe e , om
a local expe ’s poin o iew, he suspec ed ic ions wi hin he esul s p esen ed
a e B2, B5 and D1. In u u e i e a ions, ins ead o sampling all ac oss he la en
space, i would be mo e app op ia e o sample only om he poin s o he space ha
co espond o eal samples. In his way, ic ional econs uc ions could be a oided.
3.5. Conclusions
This case s udy has p esen ed a me hod based on he VAE model o ex ac he
mos common building ypologies om a digi al land and eal es a e cadas e. The
wo k has ocused on he Se ille cadas e as a case s udy o es ablish a
p oo -o -concep . The app oach di e s widely om con en ional shape clus e ing
analysis and o e s a se ies o ad an ages ha a e speci ic o he p oblem a hand.
Fi s , no p io knowledge o he ypes wi hin he da ase is equi ed. Fo example,
he numbe o clus e s does no need o be speci ied be o ehand. In ac , he ou pu
is no amed in e ms o a igid se o clus e s, bu a he displays a g adual
ansi ion be ween lea n ca ego ies. Second, less common building ypes ha ha e
li le p esence in he ci y a e il e ed ou o he ex ac ion by de aul ; since neu al
models lea n by i e a i e p ocesses o loss op imisa ion h ough epe i ion,
non- ep esen a i e samples a e na u ally punished ou o he lea ning space. And
hi d, he me hod allows o he compu a ion o sub le di e ences wi hin
ca ego ies, ende ing mul iple a ia ions o he same clus e . This is due mainly o
he abili y o VAEs o pick up shape a ia ions (such as, bu no limi ed o, scale
and o a ion) du ing he lea ning p ocess, as discussed ea lie in he Me hodology
Sec ion. O e all, he ollowing conclusions can be de i ed om his s udy:
• The me hod p oposed is e y sensi i e o he da a augmen a ion ac o .
La ge da ase s ha esul om s onge augmen a ion ac o s do no
necessa ily imp o e he lea ning cu es. This sensi i i y is a well-known
phenomenon in deep lea ning, and comp ehensi e e iews ha e been
published add essing he p oblem [265].
• The models ha e been ained o a deg ee o accu acy jus enough o p o e he
alidi y o he me hod. F om an op imisa ion pe spec i e, he e is g ea oom
o imp o emen o he models implemen ed in his wo k.
• The mos common ypologies ha e been success ully ex ac ed (a o al o 10).
A subs an ial numbe o less ob ious ypologies ha e also been ex ac ed (a
o al o 14 o 16 ypes depending on c i e ia). And up o h ee o he ypes a e
suspec ed o being gene a ed a i icially by he model ( ic ional). A plausible
81
solu ion o iden i y hese ic ional ypologies could be implemen ed by
acking he la en space dis ance om each ypology o i s closes aining
sample. This dis ance would p o ide a me ic o he ‘ ic ionali y’ o he
building ypes ex ac ed.
• The esul s show ha he me hod p esen ed is a sui able al e na i e o
con en ional shape clus e ing in he con ex o u ban ypologies, and as such,
u u e wo k should expand and consolida e his esea ch.
As a las ema k, his wo k is hoped o ha e a posi i e impac on he ield o
seismic eme gency and elie . By p o iding ools ha alle ia e he bu den o
iden i ying and modelling en-masse he s uc u al beha iou o buildings in u ban
a eas, g ea bene i s can be p o ided o hund eds o ci ies wo ld-wide, no only
wi h ega d o economic sa ings, bu also, and mos impo an ly, in e ms o
human li es.
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4. Gene a i e A i icial In elligence in Design
This chap e ocuses on Gene a i e AI and i s connec ion o he ield o design. As
men ioned a he ou se o his hesis, hose aspec s in A chi ec u e ela ed o
aes he ics ( enus as) cons i u e he mos challenging applica ion scena ios o AI. In
he las decade, he ield o ML has wi nessed a pa icula e olu ion on his on .
The de elopmen o Va ia ional Au oencode s (VAE) and Gene a i e Ad e sa ial
Ne wo ks (GAN) in 2014, ha e opened up an ocean o possibili ies o he
in e ac ion be ween AI, C ea i i y and Design. These wo models shocked he
wo ld wi h hei abili y o ‘c ea e’ ic ional, ye ex emely ealis ic, images o
a ious kinds. Among hem, hese models we e capable o gene a ing aces o
nonexis en celeb i ies wi h a ema kable eel o e aci y [267]. Thei success,
exempli ied by he la e and o he equally imp essi e expe imen s (i no mo e),
ha e consolida ed in he bi h o wha is cu en ly known as Gene a i e AI.
O cou se, such de elopmen s spu ed in ense deba es (and con inue o do so)
in A , Philosophy, and Design ci cles, bu also in he AI communi y i sel .
Impo an subjec ma e s like he idea o au ho ship o c ea i i y saw signi ican
uphea al wi h each elease o he e e -inc easingly s unning esul s coming om
hese gene a i e AI models. Gi en ha he ele ance o he opic is clea , he nex
sec ions aim o del e u he in o he connec ion be ween gene a i e AI and he
ield o A chi ec u e and Design. I should be no ed, be o e mo ing ahead, ha
ano he impo an lagship has ecen ly joined he lee o gene a i e AI; namely,
La ge Language Models (LLM). Howe e , his chap e will conside only
gene a i e models o ien ed o wo k wi h non-symbolic da a (e.g., pixels) and no
hose ha ocus mainly on seman ic inpu , like LLMs. The eason is ha some o
he main challenges acing he collabo a ion be ween AI and Design is based
p ecisely on he b idging o senso y pe cep ion and concep ual easoning; he
senso y pa , o cou se, equi ing he abili y o analogue senso y da a, i.e.,
non-symbolic da a. I should be no ed ha he mos ecen esea ch in his ield
combines LLMs a chi ec u es wi h non-symbolic models like VAEs o GANs, and
he e o e one mus no abide by his dis inc ion oo s ic ly.
4.1. Backg ound
The possibili y o building c ea i e machines o machines wi h he abili y o
au onomously gene a e hei own a e ac s has cap u ed he imagina ion o
esea che s and scien is s since he ea ly days o AI. Much o he ini ial
83
in es iga ions e ol ed a ound he ques o a i icial o au onomous ‘c ea i i y’
a he han speci ically honing on he no ion o ‘gene a i e’ machines o gene a i e
AI. In ac , he e m gene a i e was associa ed wi h sligh ly di e en ideas in AI
un il no so long ago.
Fo example, in 2010, a Ph.D. hesis unde he i le ‘Gene a i e AI’ [268] held
me ely a ain connec ion o wha is ac ually known as Gene a i e AI nowadays.
Ins ead, he wo k hinged on neo-Cybe ne ics and he need o an AI pa adigm
ha , in i sel , was able o ‘gene a e’ in elligen sys ems. Fu he mo e, he 1980s saw
he eme gence o he esea ch a ea ‘AI-based Gene a i e P ocess Planning’
[269,270]. The wo ks in his a ea we e aimed a cap u ing in a compu e p og am
he logic used by a p ocess planne o con e design in o ma ion om enginee ing
d awings o p ocess plans. Ano he a ea o gene a i e s udies, especially in
enginee ing and design, was spea headed by models ea u ing au onomous agen
ensembles. Fo ins ance, a pape om 2002 [271] desc ibes si ua ed cogni ion as he
basis o g oup c ea i e design, which is implemen ed h ough a mul iagen model.
Ano he , om 2007 [272], explo es gene a i e designs h ough an in e ac i e and
e olu iona y sys em wi h ML. Al hough he e is no ques ion abou he ‘gene a i e’
capaci ies o agen -based app oaches, especially in he ealm o A chi ec u al
Design, his a ea de ia es om he co e me hods o mode n Gene a i e AI. Finally,
some ea ly a emp s we e also made, e en p io o he wo ks men ioned abo e, in
he ield o language. A good example can be ound in he cha bo ELIZA [273],
which p ecedes he gene a i e g amma s udies ha a e discussed below.
In con as , esea ch ha ocusses on c ea i i y appea s o be mo e in line wi h
con empo a y s udies in gene a i e me hods. Also, his a enue in ol ed deepe
and mo e undamen al ques ions pe aining o AI as a whole and, as such, was
backed by a b oade communi y o enown scien is s (Ho s ad e , Rowe,
Ma indale, e c.). The pu sui o c ea i i y was seen by hese au ho s as an
impo an pa o he la ge ques ion o in elligence. In he wo ds o Rowe and
Pa idge: ”In elligence in ol es c ea i e beha iou . Few would challenge his
s a emen , bu ag eemen on wha is mean by ‘c ea i e beha iou ’ would be much
ha de o ind...” [274]. Due o how cen al c ea i i y was pe cei ed in ela ion o
he undamen al ques ion o in elligence, impo an e o s we e pu in o his opic.
A pa icula ly in e es ing legacy om hose days is an accoun o i e condi ions
o c ea i e beha iou p oposed by he a o emen ioned au ho s. A b ie ou line o
each one is copied below o e e ence, as i p o ides a use ul amewo k upon
which o discuss some o he mo e ecen wo ks la e in his hesis:
• Fi s ly, i is necessa y ha knowledge is o ganised in such a way ha he
numbe o possible associa ions ( he c ea i e po en ial) is maximised.
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• Secondly, i is necessa y o ole a e ambigui y in ep esen a ions.
• Thi dly, he e is a need o mul iple ep esen a ions.
• Fou hly, he use ulness o new combina ions should be assessable. I is o no
use o c ea e many combina ions i hey a e all useless.
• Las ly, any new combina ions need o be elabo a able o ind ou hei
consequences. [...] The consequences disco e ed should be applied o he
p oblem si ua ion; he use ulness o a disco e y is decided by i s applicabili y.
Following is a selec ion o ini ial e o s in a i icial c ea i i y ha align wi h he
p e iously men ioned di ec ions. Some o he i s a emp s on c ea i i y ook place
in he ield o language and language-o ien ed domains. Fo example, in [275,276],
gene a i e language p og ams we e de eloped wi h explici suppo o syn ax and
g amma ules. In [277,278], gene a i e expe imen s we e ca ied ou in he ield o
music composi ion. All o hese wo ks had inco po a ed an elemen o andomness
in hei gene a i e engines, which made hem e y in e es ing a i s bu a he
shallow a he end o he day. He e is a ex c ea ed by Rac o [276] in 1984:
”Bill sings o Sa ah. Sa ah sings o Bill. Pe haps hey will do o he dange ous
hings oge he . They may ea lamb o s oke each o he . They may chan o hei
di icul ies and hei happiness. They ha e lo e bu hey also ha e ypew i e s. Tha
is in e es ing.”
O he mo e popula one:
”Re lec ions a e images o a nished aspi a ions.”
As Rowe poin s ou , c ea i i y equi es a sense o no el y, which some imes
can be achie ed by in oducing andomness in he same way ha Rac o was buil .
Howe e , in his own wo ds, i seems ha ”no el y is no enough”. This is a e y
in e es ing s a emen in ligh o he cu en de elopmen s in Gene a i e AI.
O he au ho s explo ed o he a eas o c ea i i y. Lena and Da is in oduced
he p og am AM [279] in 1982, which was buil wi h he in en ion o disco e ing
ma hema ical concep s au onomously. O he s udies ha con ibu ed o his o
simila models can be ound in [280,281]. Disco e y was also a emp ed in he
domain o undi ec ed g aphs by Eps ein [282]. O he a eas o c ea i i y esea ch
included me a- ule-based models [283] and analogy-based models [284]. Las ly,
o he app oaches we e mo e lenien owa ds decen alised and connec ionis
app oaches, wi h impo an con ibu ions om Ho s ad e [285] and Minsky [286].
Fo ins ance, Rowe p oposed he GENESIS model [287], which was oo ed in
Minsky’s in luen ial ‘Socie y o Mind’ [288]. As a inal ema k, i is in e es ing o
85
e iew some o he hough s sha ed back hen on connec ionis sys ems and hei
abili y o become gene a i e. As Rowe w i es:
”These ne wo ks a e gene ally used o model e y low-le el beha iou such
as ision. Whils hey a e good a gene alising om a gi en da a se , he lea ning
p ocedu es a e e y a i icial and much esea ch is s ill needed be o e connec ionism
could be applied o he la ge p oblems o c ea i i y.”
All in all, he majo i y o hese e o s we e app oached om he pa adigm o
symbolic AI (wi h he ew connec ionis excep ions men ioned). In such models,
c ea i i y is seen unde a combina o ial pe spec i e. Al hough all o hese models
a e di e en in he way symbols a e combined o o m new s uc u es, hey a e
ul ima ely simila in hei combina o ial na u e. Some me hods, usually based on
ee-like knowledge ep esen a ion schemes, such as he COBWEB algo i hm [2],
did p esen a hyb id s a egy o combina ion and in e pola ion o achie e gene a i e
abili ies. O he ones, like FCA, can also p esen gene a i e capabili ies wi h ease.
Howe e , all o hese me hods ope a e unde he symbolic pa adigm and he e o e
s uggled g ea ly when dealing wi h senso y da a o igina ing in analogue sou ces
(e.g., pixel-based images).
4.1.1 The connec ionis leap o wa d
Wi h he inc ease in compu a ion powe and aining da a a ailabili y du ing he
2000s, neu al ne wo k models began o make impo an s ides in he a ena o ML.
By he mid-2010s, acial ecogni ion had become an indus y s anda d a e he
in oduc ion o AlexNe in 2012 [289]. I was clea hen ha he connec ionis
pa adigm excelled in he domain o aw senso y da a. Soon a e , as men ioned
ea lie , wo powe ul gene a i e models we e p oposed: VAEs we e published in
2013 [260], and GANs in 2014 [290]. VAEs we e b ie ly in oduced in he p e ious
chap e and will be explained in mo e de ail in he ollowing sec ion.
GAN model consis s o wo ne wo ks ha a e ained oge he ; one is sampling
new ins ances om poin s o a la en space, while he o he is an encode lea ning
o disc imina e he gene a ed ins ances ( akes) om he examples in he aining se .
When he gene a o is capable o p oducing ins ances ha he disc iminan canno
dis inguish om ue examples, hen he GAN has achie ed success ul aining. A
use ul analogy o unde s and GANs is ha o he police and he hie . The hie
(gene a o ) is p oducing coun e ei s o bank no es and he police (disc iminan )
has o de ec coun e ei s. Since he de elopmen o hese wo models, he ield
o Gene a i e AI has igge ed a landslide o imp essi e de elopmen s and is s ill
ope a ing in ull swing oday.
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The i s de elopmen s aimed o enhance he quali y o he images gene a ed
by hese models. The lowes hanging ui in his ega d in ol ed he use o deep
con olu ional a chi ec u es wi hin GANs [291] and VAEs [292]. Howe e , in 2017,
he size a which hese models we e able o ec ea e quali y images was only abou
256×256 pixels [267]. In 2019 he BigGAN model [293] pushed he bounda ies o
high-quali y image gene a ion o 512×512 pixels wi h esul s ha we e, in many
cases, indis inguishable om eal images. Ano he in e es ing a ea o explo a ion
was S yle T ans e , an implemen a ion o ans e lea ning ha could also be seen as
a o m o wha is known as condi ional gene a ion. This app oach used gene a i e
models o lea n ep esen a i e pa e ns ac oss a se o uni o m-s yle images, and
hen applied hese ne wo ks o images o a di e en s yle. In doing so, he ne wo k
was able o p oduce he same image ec ea ed in he s yle ha i had p e iously
lea n . Among he i s wo ks o achie e signi ican esul s a e Pix2Pix [294],
CycleGAN [295] and S yleGAN [296]. An added ad an age in hese wo ks was he
possibili y o inc ease he ou pu esolu ion using he new inpu image as a so o
sca olding. Fu he i e a ions o hese models, like S yleGAN2, also consolida ed
he applica ion o gene a i e models o image upsampling asks. In a sho ime,
hey eached esolu ions abo e 1024×1024 pixels.
An impo an a ea o esea ch in he ield was ha o disen angled
ep esen a ions. Disen angled lea ning is a machine lea ning app oach aimed a
sepa a ing dis inc , in e p e able ac o s o a ia ion wi hin he da a in o
indi idual, independen componen s o dimensions. Acco ding o Bengio e al.
[297], in a disen angled ep esen a ion indi idual la en uni s (e.g., he di e en
dimensions o he la en space) espond o changes in single gene a i e ac o s
while emaining ela i ely una ec ed by a ia ions in o he ac o s. Fo example, a
model ained on a 3D objec da ase migh de elop la en uni s ha independen ly
espond o ac o s such as objec iden i y, posi ion, scale, ligh ing, o colou . In such
a ep esen a ion, unde s anding one ac o can gene alise o new combina ions o
o he ac o s. These de elopmen s [298,299,300] ha e been c i ical in p o iding
mo e con ol when exploi ing he gene a i e abili ies o hese models, especially in
conjunc ion wi h seman ic p omp s and que ies. An ea ly example can be ound in
he (la en space) ec o a i hme ic o isual concep s implemen ed in he wo k o
Rad o d e al. in 2016 [301] (Fig. 4.1). In hei wo k, he au ho s expe imen ed wi h
ec o ope a ions in la en ep esen a ions o wo ds p oposed in [302], achie ing
e ec i e isual ope a ions. Disen angled ep esen a ions ha e made impo an
s ides, since hese wo ks, bo h in quali y and esolu ion, a e an impo an pa o
he cu en ools a ailable in he gene a i e AI indus y. A mo e in-dep h e iew o
ecen de elopmen s can be accessed in [303].
Ano he ele an line o explo a ion came abou h ough he pu sui o neu al
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Figu e 4.1: Resul s o ec o a i hme ic o isual concep s in he la en space.
disc e e ep esen a ion lea ning (also known as quan ised la en space lea ning).
Quan ised models seek o lea n a disc e ised ep esen a ion o he la en space.
This can be use ul, o example, when he con inuous space o la en a iables
needs o be mapped on o a symbolic o seman ic s uc u e o use in ano he
model. The ele ance o hese possibili ies, especially in combina ion wi h
disen anglemen , is ha hey enable a ai deg ee o composi ionali y, wi h some
in e es ing ex - o-image examples capable o gene a ing, say, a ho se wi h
elephan legs. A landma k con ibu ion in his space is VQ-VAE [304], whe e he
p oposed model is based on p e ious wo k on Vec o Quan isa ion [305]. I
achie es high-quali y images, ideos, and speech and is ela i ely easy o ain. In
hei me hod, he p io (e.g., he imposed dis ibu ion on he la en space) is no
s a ic bu is lea n dynamically du ing aining. Wi h his s a egy, he model
makes ano he impo an con ibu ion: VQ-VAE sol es he p oblem o pos e io
collapse in VAEs. Pos e io collapse is a phenomenon obse ed in powe ul VAE
models whe e he ne wo k is capable o lea ning o econs uc he inpu s wi h
negligible e o , causing he la en space o collapse in o a single poin o a e y
na ow a ea. Some o he me hods o a oid his issue ha e been published in he
li e a u e, as i s ill cons i u es an ac i e a ea o esea ch [306,307,308]. VQ-VAE
has opened a line o esea ch wi h subs an ial impac in he ML communi y.
Fu he con ibu ions can be ound in [309,310] (including a disc e e hie a chical
app oach), wi h some impo an comme cial applica ions buil on op o i s
ounda ional ideas [311].
Mo eo e , o he impo an s udies we e ad ancing he ield in di e en
di ec ions. Au o- eg essi e models we e p oposed in 2016 based on p e ious wo k
[312,313,314] and we e implemen ed in he p ojec s PixelRNN and PixelCNN
[315,316]. In he au o- eg essi e app oach, each elemen (e.g., pixel) is gene a ed
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one a a ime based on p e iously gene a ed ones. Mo e speci ically, hese models
gene a e da a sequen ially by modelling he condi ional dis ibu ion o each
elemen gi en he p e ious elemen s. The low-based model was de eloped
h ough he wo k o Rezende and Mohamed [317] in 2015. As opposed o he VAE
and he GAN models, hei p oposal hinges on building adap able dis ibu ions in
he la en space ha can be e i he a ge da a (mo e on his opic in he Me hods
Sec ion).
La e , in 2020, wo o he me hods we e eleased in he Gene a i e AI space.
Taking inspi a ion om s a is ical physics, ene gy-based models ha e been a ound
since he ea ly days [318], bu hey began o a ac mo e a en ion in ecen yea s
[319]. These models p o ide a uni o m amewo k o bo h p obabilis ic and
non-p obabilis ic me hods, and as such can be iewed as a gene alisa ion o mos
p obabilis ic me hods. In hese me hods, he e is no dis ibu ion no malisa ion
imposed on he la en space, and he e o e hose p obabilis ic models ha do
impose a no malised dis ibu ion can be seen as a pa icula case. The elease o
his cons ain o e s many ad an ages, bu also some disad an ages. Speci ically,
he p ocess o sampling new ins ances becomes less s aigh o wa d (i in ol es an
i e a i e p ocess based on Lange in dynamics [320]). Among he ad an ages, i
may be highligh ed ha (i) ene gy-based models ea u e buil -in composi ionali y
wi h o he models and also, (ii) while in bo h VAEs and Flow-based models he
gene a o mus lea n a map om a con inuous space o a possibly disconnec ed
space con aining di e en da a modes (which equi es la ge capaci y and may no
be possible o lea n), ene gy-based models can easily lea n o homogenise disjoin
egions. Due o he s ong bene i s o he model, in ense esea ch is cu en ly
ongoing in an e o o b idge he esul s gap wi h o he me hods in he ield.
The o he model also d awing inspi a ion om Physics is he Denoising
Di usion P obabilis ic Model [321], also known as Di usion Model o sho . In
essence, his model ope a es by p og essi ely adding Gaussian noise o he
aining da a, e ec i ely co up ing i . The model is hen ained o econs uc he
o iginal da a by e e sing he noising p ocess. Once aining is comple e, i can
gene a e new da a by sampling andom noise and applying he lea n denoising
p ocess o i . The me hod is seen by he au ho s as a gene alisa ion o
au o- eg essi e models. Some ad an ages o he di usion models a e aining
s abili y, high-quali y, di e se ou pu s, ease o aining, and a lowe endency o
o e i ing han in he mains eam gene a i e models. Due o hei high e iciency,
his me hod has seen an epic explosion o esea ch and indus y-led applica ions
ac oss he boa d a a e y apid de elopmen pace. Fo example, popula
pla o ms o AI-gene a ed ex - o-image g aphics, such as S able Di usion o
Midjou ney, employ i . Mo e wo ks on his app oach include (i) he La en
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Kullback-Leible di e gence (KL) be ween he dis ibu ion (no mally a Gaussian
dis ibu ion) o choice and he ob ained dis ibu ion:
Loss =Loss(X,X′) + KL
whe e,
KL =
n
∑
i=1
σ2
i+µ2
i−log(σi)−1
and,
Z=Gaussian(σ,µ)
This leads o he gene alisa ion posed abo e, whe e he loss unc ion is
exp essed as a unc ion o bo h he la en and he ou pu a iables.
This s aigh o wa d app oach makes VAEs good candida es o ea ly-s age
expe imen a ion. O he models like he e y popula GAN o Di usion Denoising
P obabilis ic Model p esen sligh ly mo e complex a chi ec u es and aining
p ocesses. Especially, he o me is known o be pa icula ly ha d o ain, and he
la e ypically in ol e leng hy and imp ac ical ou pu gene a ion imes.
Addi ionally, bo h o hese me hods in ol e a g adual composi ion p ocess o
images om andom Gaussian noise. This echnique may wo k well o some
ypes o da a, like pixel-based images, bu may no be as sui able o o he domains
ha a e o less con inuous na u e. Fo example, in he a chi ec u al domain,
building s uc u es can be de ined as g aph s uc u es; a se ies o in e connec ed
columns and beams. This g aph-like ep esen a ion will be chosen o he case
s udy p esen ed la e in his chap e , and he e o e a VAE model ha does no
in oduce his kind o Gaussian noise decomposi ion may be be e sui ed o he
expe imen a ion. O he me hods like he Flow-Based models o Ene gy-Based
models discussed ea lie ha e impo an ad an ages; howe e , hei complexi y
and less ma u e phase o adop ion may ende hem mo e sui able o a u u e
phase o expe imen a ion.
Ano he impo an opic o discuss wi h ega d o he idea o la en a iables
and la en spaces wi hin he con ex o gene a i e models is he subjec o
disen anglemen . As men ioned abo e, la en a iables can be use ul in cap u ing
ea u es in he da a ha a e no explici ly p o ided du ing aining. Fo example,
one may hope ha in a deep lea ning a chi ec u e, he sequence o hidden laye s
will e ec i ely lea n a ce ain le el o g anula i y o ea u es; he deepe he laye ,
he highe he le el o abs ac ion o he ea u es cap u ed. Ve y deep laye s could
de ec , o ins ance, a ce ain di ec ion o some ela i e posi ioning, while mo e
shallow ones could de ec a pa o he mou h o he eye. This hypo hesis has been
96
in ensely explo ed h oughou he deep lea ning pa adigm, deli e ing mixed
esul s [334,335,336]. Yes, his phenomenon does ake place o a easonable
deg ee, bu a he same ime, i is ex emely ha d o p edic wha laye s will
cap u e wha and o wha ex en . In ac , he na u e and abs ac ion le el o he
ea u es collec ed a each laye a e e y sensi i e o he design o he model and he
aining da a (including he o de in which he samples a e ed in o he ne wo k).
Consequen ly, hey a y widely om one ne wo k con igu a ion o he o he ,
lea ing he modele wi h a he limi ed con ol o e he p ocess. Some wo ks ha e
explo ed he ea u es lea n inside he hidden laye s o deep lea ning models in
e y c ea i e ways. An example can be ound in he p ojec known as ‘Deep
D eam’ o ‘Incep ionism’ [337], whe e hese ea u es we e used o econs uc
ema kably su eal images.
Simila ly, one would hope ha by se ing up a se o la en a iables (dimensions
o he la en space), he model will i hose ea u es implici in he da a ha a e
mos p ominen o each o he dimensions o he la en space. While his is pa ially
ue (and mo e so a e he me hods Be aVAE [298], Fac o VAE [300] and In oGAN
[299] among o he s), i is also subjec o he same ca ea s as in he case o deep
lea ning. Indeed, hese wo ks do p esen an impo an deg ee o disen anglemen
ha deli e s e y signi ican esul s. Howe e , he e is s ill li le di ec con ol o e
wha ea u es make i o each o he dimensions in he la en space. Addi ionally,
he con igu a ion o he ne wo k, ha is, he size o he la en space, is no a lexible
pa ame e capable o adap ing o he inpu samples. Once a la en space size is se ,
he model will be ained (wi h massi e amoun s o da a) wi h he gi en size om
beginning o end. As a consequence, he amoun o implici disen angled ea u es
ha can be po en ially cap u ed by he model is limi ed by he size o he la en
space.
4.3. Li e a u e e iew: (a chi ec u e- ela ed)
As men ioned in he p e ious sec ions, c ea ing new ins ances based on he
in o ma ion o known e e ences is a classical necessi y wi hin design disciplines.
F om an ini ial known design, i could be desi able o p ese e some o i s ea u es
by ‘impo ing’ hese in o a amily o new designs, concei ed as a ia ions o he
o iginal. Gene a ing his amily o new designs is a ask ha can be add essed wi h
ei he manual o compu a ional me hods. Howe e , one could a gue ha bo h
ypes o me hods could be ‘algo i hmically’ add essed: by iden i ying he design
ea u es ha one may wish o p ese e (so ha hey a e ound wi hin he ins ances
o he new amily o designs), a se o ules can be speci ied so ha he selec ed
ea u es a e applied wi h di e en g adien s, making each ins ance unique, ye
97
iden i iable as pa o a amily o shapes design [338].
Howe e u ili a ian, ools o his na u e may suppo he c ea i e p oduc ion
wi hin design disciplines by o e ing a dynamic way o ob aining a ia ions o he
known e e ence o u he e alua ion. In pa icula , and in con as wi h a wide
s eam o ML esea ch ha ocusses on 2D p oblems, he applica ion o ML o he
a chi ec u al a ena demands a 3D app oach. In his ega d, machine lea ning
echniques o 3D shapes a e implemen ed in a ious di e en asks o geome y
manipula ion o e alua ion pu poses. These asks can be classi ied in o he
ollowing ca ego ies: Single objec classi ica ion [339,340], 3D pose es ima ion
[341], mul iple objec s de ec ion [342], scene-objec seman ic segmen a ion [343],
3D geome y syn hesis- econs uc ion [344] and many o he ca ego ies ha a e
se iceable o he echnical aspec s o wo king wi h 3D geome y.
Ini ially, some machine lea ning esea ch p ojec s ackled he p oduc ion o 3D
objec s h ough echniques associa ed wi h deep-gene a i e models ope a ing wi h
2D da a se s. In his app oach, a geome ic 3D en i y can be econs uc ed om he
in o ma ion acqui ed om he 2D ou pu o he model [345,346,347]. Fo example,
one implemen a ion o his echnique in he ield o a chi ec u al design, o
gene a e new ins ances o 2D g aphs ep esen ing a chi ec u al layou s o li ing
uni s, inds inspi a ion in ‘composing high pe o ming pa s o sepa a e design
en ies in o a new whole’ [348]. This s a egy akes ad an age o he ela i e
consolida ion o well- es ed models applied o 2D pixel da a. While in many
occasions hey emain a he le el o images (in e io deco a ion s yles o s yle
ans e on building acades, e c.), in some o he s hey le e age hem in
combina ion wi h o he echniques so as o become unc ional in he 3D domain.
Howe e , he e a e also a good numbe o s udies ha add ess 3D p oblems
di ec ly, wi hou in e media e 2D models. The ollowing is a e iew o some o he
mos ele an wo ks along his line in he con ex o he case s udy de eloped in
he nex sec ion.
In 3D s udies o a chi ec u al designs and o ms, ep esen a ion is a key
elemen . Pixel-based o oxel-based ep esen a ions can ha e signi ican
limi a ions in enginee ing and a chi ec u al design. Especially in a chi ec u al
design, he la ge scale and complexi y o a e ac s can make oxel-based
app oaches p ohibi i ely compu a ionally expensi e, e en wi h ad anced
compu ing ha dwa e. The e o e, esea ch e o s ha e been dedica ed o he sea ch
o sui able al e na i es. In e ms o da a ep esen a ion, some wo ks ha e a acked
his p oblem pu ely om a ML pe spec i e, aside om any gene a i e aspec s. A
sample o hese wo ks includes (i) MeshCNN [349], (ii) VoxNe : A 3D
Con olu ional Neu al Ne wo k o Real-Time Objec Recogni ion [339] and (iii)
98
Gene a i e Deep Lea ning in A chi ec u al Design (GDLAD) [350], all o hem a e
in e es ing app oaches ha look a he p oblem om di e en angles.
MeshCNN p oposes a wo k low in which 3D objec s a e ep esen ed as
e ahed on meshes, and he connec i i y o he edges o each mesh in o ms he
a chi ec u e o he model, accoun ing o he size o he con olu ional laye . In his
model, meshes a e nonuni o m ep esen a ions o he shapes. Since hese a e
essen ially numbe ed poin clouds, he objec s esul in i egula s uc u es. In
con as , in he wo k o bo h Ma u ana (VoxNe ) and New on (GDLAD), he 3D
objec s p esen in he da a se a e deno ed in a consis en ly sized 3D en elope,
using oxels wi hin his 3D space. The case s udy ha will be p esen ed la e elies
hea ily on ec o s deno ing he connec ions be ween poin s o a wi e ame
s uc u e in 3D space. Thus, i sha es impo an s a egic simila i ies wi h
MeshCNN as opposed o he la e wo ks (VoxNe and GDLAD).
Wi h ega d o con ibu ions pu ely in he ield o Gene a i e AI, he ollowing
wo ks ha e been selec ed on he basis o hei simila i y in he objec i es o s a egy
o he la e case s udy:
In ”3D Shape Syn hesis o Concep ual Design and Op imiza ion Using
Va ia ional Au oencode s” [351], a da a-d i en 3D shape design me hod is
p esen ed. I can lea n a gene a i e model om a co pus o exis ing designs and
use his model o p oduce a wide ange o new designs. The app oach is based on
an unsupe ised VAE a chi ec u e o lea n an encoding o he samples in he
aining co pus, wi hou he need o an explici pa ame ic ep esen a ion o he
o iginal designs. To acili a e he gene a ion o smoo h inal su aces, he me hod
uses a 3D shape ep esen a ion based on a dis ance ans o ma ion o he o iginal
3D da a, a he han using he commonly u ilised bina y oxel ep esen a ion (as in
VoxNe ). The gene a o maps he la en space ep esen a ions o he
high-dimensional dis ance ans o ma ion ields, which a e hen au oma ically
su aced o p oduce 3D ep esen a ions. The me hod is applied o he
compu a ional design o glide s ha a e subsequen ly op imised o achie e a
ce ain physics-based pe o mance.
Ano he con ibu ion ”Au oma ed modula housing design using a module
con igu a ion algo i hm and a coupled gene a i e ad e sa ial ne wo k (CoGAN)”
[352], in oduces an inno a i e app oach o he design o modula housing. I uses
an au oma ed sys em ha uses a module con igu a ion algo i hm and a coupled
gene a i e ad e sa ial ne wo k (CoGAN). The module con igu a ion algo i hm
au oma es he a angemen o di e en modules based on speci ic design c i e ia
and cons ain s, ensu ing op imal spa ial con igu a ion and unc ionali y. Then, he
CoGAN a chi ec u e consis s o wo GANs wo king oge he ; one GAN gene a es
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a chi ec u al designs, while he o he e alua es and e ines hem o ensu e quali y
and cohe ence. The p oposed me hodology aims o s eamline and imp o e he
modula home design p ocess, making i mo e e icien and adap able o a ious
design equi emen s, showing ha he sys em can p oduce di e se and inno a i e
modula home designs ha mee he speci ied equi emen s. The gene a ed
designs we e e alua ed o easibili y and aes he ic appeal, showing p omising
po en ial o eal-wo ld applica ion.
The wo k ”Di usion P obabilis ic Model Assis ed 3D Fo m Finding and
Design La en Space Explo a ion” [353], employs di usion models o he
gene a ion o no el designs. The me hod is applied o he spa ial ans o ma ion o
Taihu s ones, a adi ional Chinese ga den elemen known o i s in ica e and
na u al o ms. The me hodology le e ages he s eng hs o di usion models o
gene a e and explo e complex 3D geome ies, enabling inno a i e design
possibili ies. The au ho s use dis ibu ions in he la en space as a ool o explo e
he space o design possibili ies, which is ac ually a common ai o all he wo ks
using models based on la en spaces. This use o he la en space allows designe s
o unco e a wide ange o po en ial o ms and ans o ma ions, os e ing
c ea i i y, and pushing he bounda ies and limi a ions o he designe ’s
imagina ion. The s udy sha es many simila i ies wi h he case s udy in his chap e .
In pa icula , i s di usion model aims o in e pola e o ganic s one o ms wi h
o hogonal building-like shapes. In doing so, he au ho s expec he model o
a i e a in e es ing blends o o ganic o ms ( esembling Taihu s ones) ha s ill
possess some deg ee o o hogonali y and a e s ill easible in e ms o physical
cons uc ion. An illus a ion o hei esul s is shown in Fig. 4.6.
A e y in e es ing con ibu ion ”VQ-CAD: Compu e -Aided Design model
gene a ion wi h ec o quan ized di usion” [354], ocusses on lea ning implici
cons ain s in he domain o Compu e Aided Design (CAD). Gene a i e models
a e na u ally equipped o pe o m con inuous ansi ions ac oss da a. Howe e , in
some da a domains, such as indus ial o a chi ec u al design, no e e y shape o
o m can be conside ed a ‘ alid’ design, since some designs migh be impossible o
ab ica e o build. Fo example, a pin-hole ha does no adhe e o he s anda d size
o ma ke -a ailable pins, o a column ha is oo hin o bea he load assigned o
i . Thus, gene a i e s udies on CAD a e ac s ha e o en led o he explici
imposi ion o ex e nal cons ain s.
An impo an aspec o hei wo k is ha i does no en o ce any explici
cons ain s on he model, bu ins ead he model lea ns hem h ough examples and
is hence inco po a ed in o he model implici ly. The me hod is based on a ec o
quan isa ion la en di usion a chi ec u e, wi h an implemen a ion o hie a chical
100
Figu e 4.6: Resul s o he Taihu s ones p ojec .
code-book in he la en space. Tha is, he me hod uses a hie a chical disc e e
app oach o he dis ibu ion o he la en space ha allows ope a ing and lea ning
wi hin a cons ained domain. Addi ionally, he app oach pa es he way o
ex -based embeddings and p omp -based in e ac ions wi h he gene a i e engine,
which hey exploi in he second pa o hei pape h ough he CLIP model. In
e ms o da a ep esen a ion, he me hod engages wi h CAD p imi i es such as
lines, a cs, ex usions, p o iles, e c., ha a e ha d-coded in he model wi h
hie a chical dependencies ( o o m he code-book). In essence, VQ-CAD does no
deal di ec ly wi h aw da a, bu ins ead, as in he app oach ha will be p esen ed
he e, he e is a p elimina y modelling o he spa ial da a ha con o ms he objec s.
Ne e heless, he me hod does p esen ele an ad ances wi h ega d o he case
s udy in his hesis, as i pu s o h an in e es ing solu ion o he p oblem o design
cons ain s.
Finally, ”3D Di usion o 3D Dis igu a ion?” [355] cons i u es wha can be
conside ed a success ul and indus y-comple e example o a gene a ion wi hin
he Gene a i e AI pa adigm. The wo k uses di usion models o c ea e design
blends ac oss a se o objec ca ego ies ( adi ional wooden chai s, u ban benches,
imbe ow-boa s, e c.). The app oach is based on a oxelised ep esen a ion o he
da a and he e a e no design cons ain s imposed. A e a isual explo a ion o he
la en space, an in iguing se o chai -like and bench-like a e ac s we e selec ed by
he a is . Subsequen ly, hese a e ac s we e digi ally ab ica ed and exhibi ed a
he CVPR 2024 AI A con e ence (Fig. 4.7).
The di e en wo ks discussed abo e highligh he ele ance o gene a i e
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Figu e 4.7: Chai a e ac s exhibi ed a he CVPR 2024 AI A con e ence.
models in he ield o design. They also show how he speci ic equi emen s o he
ield call o di e en da a ep esen a ion s a egies. As poin ed ou be o e, while
many o he mos impo an miles ones and achie emen s in ML and Gene a i e
AI ha e been showcased on pixel images, his ep esen a ion medium may p esen
impo an limi a ions in he domain o enginee ing and a chi ec u al design.
Pa icula ly o a chi ec u al design, he inhe en la ge scale and complexi y o he
a e ac s may ende oxel-based app oaches compu a ionally expensi e, e en
wi h he immense capaci y o cu en compu ing ha dwa e. Thus, o he me hods
o ep esen a ion need o be explo ed. In he ollowing sec ion, a case s udy is
p esen ed o he in e pola ion o building ypes. In his s udy, he buildings a e
exp essed as ma hema ical g aphs ha ca y he in o ma ion on how he beams
and columns a e connec ed o each o he . This app oach di e s om he s a egies
discussed abo e and may p o ide a alid al e na i e o he s udy o gene a i e
me hods o a chi ec u al building s uc u es.
4.4. Case s udy: VAE o he gene a ion o hyb id building
ypologies
4.4.1 In oduc ion
In design disciplines, he need o al e na i es o a known design is a classic
si ua ion. I mani es s i sel as a sea ch o a ia ions ha can esemble ce ain
cha ac e is ics o he o iginal known design, whils being o iginal in hei own
igh . Deep gene a i e models can help ackle such challenges by p oducing
ou pu samples ha esemble ea u es o he inpu sample. Being p obabilis ic
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models, hey allow o in e p e able ep esen a ions and measu able ou pu
p edic ions, in addi ion o he adap abili y and lea ning scalabili y o deep neu al
ne wo ks. This esea ch a ea is one o he mos exci ing and apidly e ol ing ields
o s a is ical machine lea ning [356].
The p esen case s udy ocusses on he use o VAEs models [357], which a e a
special kind o au oencode ha en o ce a con inuous dis ibu ion in hei la en
space. As explained ea lie , by sampling om a con inuous la en space, hese
models gene a e new objec s ha inhe i ea u es om he samples p esen in he
aining se bu a e a he same ime essen ially unique. This s udy ollows on
p e ious wo k whe e he no ion o a ‘connec i i y ec o ’ was de eloped [358],
which ep esen ed he geome ic 3D objec in a ne wo k ashion. This encoding
esul ed in a da a se o high-dimensional ec o s.
Using he way da a a e encoded, geome ic 3D objec s can be exp essed as
enso -shaped inpu da a se s o aining. Thus, he challenge becomes he balance
o he la ge numbe o pa ame e s in he model, especially when compa ed o he
amoun o samples in he aining se . The wo k p esen ed in his sec ion handles
inpu composed o high-dimensional ec o s con aining he da a o geome ical
objec s. These objec s will be called ’building ypes’, as hey a e simpli ied
ep esen a ions o he geome y o mo e sophis ica ed a chi ec u al building
objec s. These a e inspi ed by he s uc u al wi e ames o hese building
geome ies. By aking a simpli ied se o cen e lines o he in e connec ed
s uc u al elemen s ha compose an a chi ec u al objec in 3D space, a wi e ame is
c ea ed. Thus, his wi e ame is ep esen a i e o he co e geome y o he building
ype. Desc ibed by connec i i y ec o s, his geome ical objec is used as inpu
da a o a VAE model, opening up a me hodology wi hin ML applied o 3D objec s
ha is applicable o he ield o a chi ec u al design.
As discussed ea lie , VAE models a e shown o be able o gene a e many ypes
o complex da a. Al hough ini ially ained on se s o 2D images, he p oli e a ion
o hese models in wide disciplines has d i en he need o wo k wi h ec o da a
and 3D geome y [359,360]. Va ious wo ks wi hin he design communi y ha map
he po en ial o his app oach ha e al eady been conduc ed [361]. Powe ul
echniques inhe en o deep-gene a i e models such as sampling [362] and ea u e
ec o a i hme ic [301] show g ea p omise in he con ex o design.
Deep-gene a i e models ypically equi e la ge da a se s o aining pu poses.
Wo king wi h ep esen a ions o s uc u al building ypes allows he
implemen a ion o pa ame ic ools o da a augmen a ion. This is because
building ypes allow indi idual samples o ha e a ious disc e e, ye obse able,
cha ac e is ics ha enable hem o be iden i ied as pa o a gi en amily o ype. In
103
he Expe imen al sec ion, an accoun o he expe imen s conduc ed is p esen ed. In
hese es s, a VAE model ains on an augmen ed da ase and lea ns o ex ac
ea u es ha a e cha ac e is ic o he inpu building ypes. In he las s age o he
p ocess, he gene a i e capabili y o he ne wo k is used by sampling new poin s
om he con inuous la en dis ibu ion ha he model has lea n . The decode hen
ou pu s hei co esponding connec i i y maps ha esul in newly gene a ed
building ypes.
This wo k is an a emp o imp o e he esul s ob ained h oughou he
expe imen s conduc ed du ing he de elopmen o his me hod [358], leading o
o e i ing o he lea ning p ocess o he model, such as he ollowing: (i) due o he
high dimensionali y inhe en o he echnique used o encoding 3D objec s, a la ge
numbe o samples we e equi ed o ain he model; (ii) limi ed geome ical
a ia ion o he ypes in aining and alida ion se s, and (iii) models wi h densely
connec ed laye s esul ed in a e y high numbe o pa ame e s (150 M+ ainable
pa ame e s). This case s udy explo es he ollowing solu ions o he
a o emen ioned p oblems: i s , he de elopmen o a pa ame ic da a
augmen a ion scheme ha enhances geome ical a ia ion. Second, he
implemen a ion o con olu ional laye s wi hin he a chi ec u e o he model,
helping o educe he numbe o pa ame e s o he model while main aining a
s ong capaci y o lea n complex pa e ns. Las ly, a cons ained a ian o he
pa ame ic augmen a ion me hod ha allows o he limi a ion o he ea u e
sp ead o he geome ies ha compose he da a se .
Fu he mo e, his s udy seeks o se e as a s a ing poin o explo ing u u e
a enues o gene a i e design, especially when in sea ch o al e na i es o a known
building con igu a ion. The main con ibu ion he e is o p o ide new insigh s in o
how pa ame ic augmen a ion echniques migh imp o e VAE lea ning in he
con ex o 3D building wi e ames. Despi e he ac ha he cu en ou pu is s ill
e y much a wo k in p og ess, he esul ing 3D wi e ames can be concei ed as he
i s s ep owa ds he in e pola ion o geome ies om a se o known inpu ypes.
Thus, his me hodology can se e o expe imen a ion and can be u he explo ed
by disciplines o a chi ec u al design. This is only a snippe o he possibili ies ha
his me hodology can unlock.
4.4.2 Me hodology
This sec ion is a anged in o se e al pa s: da a ep esen a ion, VAE, and ne wo k
a chi ec u e. In he i s pa , a de ailed desc ip ion o he me hods used o da a
ep esen a ion is p esen ed, ollowed by a desc ip ion o he encoding me hod based
on he concep o a 3D-can as wi h oxelised wi e ames. Then, a desc ip ion o he
104
e ised neu al ne wo k a chi ec u e used is shown. The model lea ns a con inuous
la en dis ibu ion o he inpu da a om which i is possible o sample and gene a e
new geome y ins ances, essen ially hyb ids o he ini ial inpu geome ies.
Da a ep esen a ion: Connec i i y map
In o de o ain a VAE, i is c ucial o p epa e he 3D geome y in a way ha can be
pa sed h ough he ne wo k. This means choosing he mos compac way o
ep esen he geome y, a oiding edundancies whils e aining ull in o ma ion.
The scheme p esen ed he e is based on a 3D-can as, which consis s o a
ec angula 3D olume disc e ised in cube-shaped cells wi hin which he inpu
geome y is con ained. Each cell o he 3D-can as con ains labelled connec i i y
ec o s ha can be ac i a ed o deac i a ed depending on he inpu geome y.
These connec i i y ec o s ep esen wi e ame segmen s in di e en o ien a ions
ha a e used o app oxima e he inpu geome y in 3D space. To keep he da a
ep esen a ion compac and wi hou o e laps, pa allel connec i i y ec o s a e
disca ded and only 13 ec o s o each cell a e conside ed, as shown in Figs. 4.8
and 4.9. To illus a e he scheme, simple geome y and connec i i y ec o s a e
depic ed in Figs. 4.10,4.11, showing he same p inciple wo king in 3D space.
inpu ec o dim = heigh x wid h x 4
A, B, C, D
4 possible connec ions be ween nodes
2D can as
inpu ec o dim = heigh x wid h x 4
A, B, C, D
4 possible connec ions be ween nodes
2D can as
B CA
D
Canopy wi h
Canopy
ec o size o ope a ions = cloudP _h * cloudP _w *4
2d Rep esen a ion
Figu e 4.8: Diag am o he connec i i y ec o scheme o a 2D geome y.
A he beginning o he ou ine, a 3D-can as is gene a ed ‘a ound’ he inpu
geome y, so ha he ull ex en o he inpu can be encoded wi hin i . Wi e ame line
segmen s o he inpu geome y a e hen snapped o he g id de ined by he cube-
shaped cells o he 3D-can as and co esponding connec i i y ec o s a e mapped
105
Figu e 4.16: Pa ame ic gene a ion o samples (CCTV).
au oencode s, o sligh ly di e en a ian s o he same ou pu . This gene a es a
much smoo he and in e pola ed la en space capable o p oducing new ou pu s
ha sha e common ea u es om di e se inpu s.
As long as he VAE model does no p o ide a single encoding bu a se o
encodings ha , wi h g ea e o lesse p obabili y, could be he esul o he encode ,
he usual loss unc ions ( ep esen a ion losses) a e no adequa e o measu e he
e o ha he ne wo k p esen s du ing aining. In o de o sol e his p oblem,
om a heo e ical poin o iew, a new ac o is in oduced in he loss unc ion,
called KL-di e gence (Kullback–Leible Di e gence) [266], which, ins ead o
measu ing he dis ance be ween poin s, measu es he di e ence be ween wo
p obabili y dis ibu ions.
112
z = μ + εσ
ε
Sample
om
N(0,1)
DKL[ N(μ,σ) | N(0,1) ]
μ
σ
+ = Loss
Recons uc ion Loss
Inpu laye
T aining se 1
T aining se 2
Hidden laye
Hidden laye
Hidden laye
La en laye
Ou pu laye
Hidden laye
Hidden laye
Hidden laye
Encode Decode
Recons uc ed se 1
Recons uc ed se 2
ReLU ac i a ion
sigmoid ac i a ion
Figu e 4.17: Gene ic diag am o he ne wo k a chi ec u e o a s anda d VAE.
As usual in machine lea ning, some condi ions can be imposed on he ne wo k
so ha i becomes able o lea n a con enien dis ibu ion (usually a Gaussian
dis ibu ion, as i o e s simplici y in he implemen a ion).
Neu al ne wo k a chi ec u e
Neu al ne wo k models p esen an ex emely high a ie y o possible
con igu a ions. To da e, he e is no s aigh o wa d me hodology o de e mine he
op imal con igu a ion o a model o a gi en da a se . Neu al ne wo k models a e
e y sensi i e o inpu da a; wha may wo k o a ce ain p oblem is likely o
pe o m poo ly o a di e en da ase . Fo his eason, he op imal se up o he
model has o be ound h ough heu is ics, wi h he added di icul y ha he sea ch
space is o e whelming. To complica e hings u he , lea ning p oblems may
equi e he use o huge da a se s, which make aining p ocesses a a he slow
endea ou and, hus, hinde he possibili y o massi e es ing h ough he sea ch
space.
Some o he mos ele an app oaches o his p oblem ha e been he
implemen a ion o heu is ics h ough gene ic algo i hms. Gene ic algo i hms allow
he space o hype pa ame e s o be sea ched in a sys ema ic way and ha e been
shown o be e y e ec i e in de e mining e icien con igu a ions o neu al
ne wo k models [365], especially when compa ed o mo e adi ional g id-sea ch
app oaches [366]. Howe e , in he p esen wo k he e is a la ge o e head in e ms
o compu a ion due o he magni ude o he p oblem ha is being deal wi h.
Wo king wi h 3D da a se s implies ha he ne wo ks ha e o lea n ea u es om
e y la ge samples, and he e o e he models mus be con igu ed in a way ha
allows o accommoda ing a high le el o complexi y ( he ne wo k mus be eady
113
o app oxima e e y complex unc ions). The combina ion o a powe ul ne wo k
a chi ec u e and a la ge da a se (+50 k samples, 1 MB pe sample) ansla es in o
highly ime-consuming aining o small es s. This ci cums ance en ails a s ong
limi a ion in he numbe o expe imen s ha may be ca ied ou in a easonable
amoun o ime, despi e employing one o he bes GPU a ailable in he ma ke .
Gi en he con ex , his ea ly s udy does no ocus on exhaus i ely sea ching o
an op imal ne wo k con igu a ion, bu a he i simply a emp s o ind a ne wo k
a chi ec u e ha is capable enough o clea ly sepa a ing geome ic ypes in he la en
space o he VAE. Finally, be o e mo ing on o he nex sec ion, Fig. 4.18 p esen s a
comple e diag am o he p oposed me hodology.
z = μ + εσ
ε
Sample
om
N(0,1)
DKL[ N(μ,σ) | N(0,1) ]
μ
σ
+ = Loss
Recons uc ion Loss
Inpu laye
T aining se 1
T aining se 2
Hidden laye
Hidden laye
Hidden laye
La en laye
Ou pu laye
Hidden laye
Hidden laye
Hidden laye
Encode Decode
Recons uc ed se 1
Recons uc ed se 2
ReLU ac i a ion
sigmoid ac i a ion
Geome y
F ee Limi ed
exac size o da ase
T aining
Dense
scheme
T aining
Con 3D
scheme
Sampling om
La en Space
New Geome ies
Figu e 4.18: Wo k low diag am o he p oposed me hodology.
4.5. Expe imen a ion and discussion o esul s
Th oughou all expe imen s conduc ed in his s udy, he sou ce da a se is ini ially
composed o 30K a ia ions o a CCTV-inspi ed building and ano he 30K
a ia ions o a Hejduk-inspi ed s uc u e. In he las expe imen s, his numbe was
inc eased o 75K a ia ions o each ype. In he aining examples gene a ed, he
3D-can as on which hese samples a e insc ibed is se consis en ly as a g id o
21×21×21 uni s. This esolu ion is su icien o dis inguish s uc u al ypes like
114
a ches, wall and su ace elemen s, olumes wi h ca i ies, openings, e c., allowing
o he design and implemen a ion o ins ances o neu al ne wo ks which a e
ained o ecogni ion and handling o da a pe aining o he ield o a chi ec u al
geome y. In all cases, he connec i i y ec o o each poin in he g id akes 13
alues. The e o e, he numbe o inpu neu ons o he VAE is
21 ×21 ×21 ×13 =120, 393. As he numbe o aining pa ame e s in a neu al
ne wo k g ows wi h he numbe o inpu neu ons, his size o he 3D-can as is
close o he limi o wha can be easonably deal wi h in e ms o a ailable
compu a ional powe .
The la en space o he VAE is always ixed o 2 dimensions (2 neu ons in he
bo leneck o he au oencode ). In VAEs, his low alue is jus i ied by he ac ha
high dimensionali y in he la en space has been shown o deli e poo esul s [357]
and has been c i icised o he e ec s o he ’soap bubble’ in he ou pu [367].
Encode s and decode s a e de ined as symme ic as possible. Regula isa ion
echniques such as d opou laye s ha e no been used because hey may
comp omise he de ini ion o he econs uc ed geome ies. The econs uc ion
e o me ic used is Bina y C oss En opy, as is commonly ecommended in VAE
models [368]. Howe e , he pe o mance o he models will also be e alua ed
quali a i ely om a design pe spec i e, since he objec i e o his esea ch is o
p o ide a gene a i e ool o design. In pa icula , he assessmen s will conside
he uniqueness and hyb idisa ion o ea u es p esen in he gene a ed geome ies.
The i s pai o es s aims o compa e he pe o mance o (i) he da a se
gene a ed by pa ame ic augmen a ion, as explained abo e, and (ii) he p e ious
augmen a ion s a egy implemen ed in [358], which is based on a combina ion o
geome y displacemen s and andom noise in he alues o he connec i i y ec o .
Fo his pu pose, bo h da a se s a e ained du ing 25 epochs unde he same
eed- o wa d ne wo k wi h only one hidden laye , o he sake o simplici y. The
encode con igu a ion has an inpu laye o 21×21×21×13 neu ons and 1 hidden
laye o 512 neu ons as seen in Table 4.1. The decode is exac ly symme ical, and
he la en space is wo-dimensional.
Inpu laye Hidden laye
(H1) La en space Hidden laye
(H1’) Ou pu laye
Type - Dense Dense Dense -
Size 120,393
(21x21x21x13) 512 2 512 120,393
Ac i a ion elu elu elu elu sigmoid
Table 4.1: Ne wo k a chi ec u e o p elimina y expe imen s.
In he case o he displacemen and noise da ase , aining yields much lowe
115
e o a es han pa ame ic augmen a ion (Tables 4.2,4.3 and Fig. 4.19). This is
unde s andable, as he spec um o geome ies enabled by he new me hod is
much mo e di e se and, hus, equi es s onge lea ning capabili ies om he VAE
model. Howe e , he la en space esul ing om he la e shows ha he ne wo k
is al eady able o di e en ia e he wo ypes o building o some ex en (Fig. 4.20),
while he la en space co esponding o he o me is a om capable o ende ing
his dis inc ion (Fig. 4.22). Fu he mo e, dis inc s uc u al ea u es can be obse ed
in he la en space co esponding o he pa ame ic augmen a ion da a se (Fig.
4.21), which a e no p esen in any o m in he o he la en space. Finally, in Fig.
4.20, VAE model was able o sp ead he samples aking a la ge po ion o he la en
space han in Fig. 4.22, whe e mos samples a e concen a ed be ween he alues
(−2.5, 2.5)on he e ical axis. Al hough hese a e pu ely isual obse a ions, i is
ad isable o app oach his analysis om a mo e igo ous me hodology in u u e
wo k, especially in cases whe e he dis inc ion is less ob ious.
Ba ch size Op imize Lea ning a e Valida ion loss Valida ion loss
(A) pa ame ic
augmen a ion
(B) andom noise +
displacemen s
128 RMSP op 0.0005 1,261.57 401.35
‘’ ‘’ 0.0010 1,246.69 400.72
‘’ ‘’ 0.0015 1,279.31 399.61
‘’ ‘’ 0.0020 1,311.84 405.06
Table 4.2: Hype -pa ame e s and esul s o p elimina y expe imen s.
T aining loss Valida ion loss
Pa ame ic augmen a ion 1242.39 1247.02
Noise + displacemen s 467.56 471.63
Table 4.3: T aining esul s o p elimina y expe imen s.
A plausible in e p e a ion o his appa en con adic ion would poin o he
possibili y ha he a ie y o he in o ma ion con ained in he da a se gene a ed
h ough andom disc e e displacemen s (which a e e y limi ed in compa ison
wi h he olume o he da a se ) and andom noise in he alues o he connec i i y
ec o is no ich enough o enable he lea ning o ele an ea u es. I he ne wo k
lea ns ea u es ha a e no ep esen a i e o he inpu , i may no be able o
sepa a e hem in a la en space e en i i succeeds in econs uc ing hem.
Acco dingly, i is concluded ha he da ase p oduced by pa ame ic augmen a ion
o e s be e p ospec s o u he aining. Howe e , i mus be no ed ha he e is
a dis inc i e ea u e ha clea ly di e en ia es he wo ypes: CCTV does no ha e
diagonal elemen s. This may gi e he VAE a head s a in he aining p ocess in
e ms o sepa a ing bo h classes in he la en space. In o de o es o gene ali y,
116
0 5 10 15 20
epochs
0
500
1000
1500
2000
2500
loss
_loss (pa ame ic augmen a ion)
_loss
_loss (noise + displacemen s)
_loss
Figu e 4.19: Bes aining esul s o bo h he pa ame ic augmen a ion da a se and he p e ious
andom displacemen s + noise da a se .
Figu e 4.20: La en space. Encoded samples om he pa ame ic augmen a ion da a se (yellow and
pu ple do s ep esen each o he wo aining ca ego ies).
117
Figu e 4.21: Highligh o obse ed s uc u al ea u es in he la en space om he pa ame ic
augmen a ion da a se .
mo e ypes should be sc u inised. Howe e , his ea ly wo k a emp s only o ca y
ou an ini ial explo a ion on he po en ial o he me hodology p esen ed he e.
Upon p oo o he po en ial bene i s o he a o emen ioned pa ame ic
augmen a ion s a egy, he second se o expe imen s a emp s o es ablish whe he
a ne wo k a chi ec u e based on 3D con olu ional hidden laye s would ou pe o m
a model con aining only linea laye s ha a e densely connec ed. Con olu ional
laye s can help keep he numbe o ainable pa ame e s in check, as will be
explained in he discussion o esul s. This is impo an because i he a io o he
numbe o aining samples is o e weighed by he pa ame e s, hen he e is a e y
high isk o o e i ing. Deep a chi ec u es can be ex emely powe ul; howe e ,
he e is a ade-o be ween he magni ude o he p oblems ha a neu al ne wo k
can sol e and he o e i ing o he ne wo k o he da a, as shown in Fig. 4.23.
Fo his se o expe imen s, wo g oups o ne wo k a chi ec u es ha e been
selec ed a e u he p elimina y es ing. The i s g oup (A-Con ) includes h ee
con olu ional schemes, and he second (B-Dense), h ee s anda d eed- o wa d
con igu a ions wi h a ying numbe s and sizes o hidden laye s. The i s model
(C21-C7-D512) o he A-Con g oup ea u es wo 3D con olu ional laye s in he
encode , leading o a linea dense laye o 512 neu ons and a symme ical decode .
118
Figu e 4.22: La en space. Encoded samples om he andom displacemen s + noise da a se .
Figu e 4.23: Model complexi y e sus aining and alida ion e o s (o e i ing p oblem).
The la en space is again 2D (and will emain he same in all he expe imen s). The
i s o he laye s is a 3D con olu ional laye spa ially a anged as 21×21×21
neu ons wi h a dep h o 13 channels. Con olu ions a e applied in 3×3×3 uni s
wi h maximum o e lap. The size o he second one is 7×7×7, and he es o he
con igu a ion emains iden ical. The second model (2xC21-2xC7-3xD512) duplica es
bo h con olu ional laye s and adds wo mo e dense laye s o 512 neu ons a he
end and beginning o he encode and decode , espec i ely. Repe i ion o
con olu ional laye s has deli e ed good esul s when applied o deep neu al
119
ne wo ks [369]. Finally, he hi d model (3×C21-3×C7-4×D512) adds ano he
con olu ional laye be ween each o he wo pai s o con olu ional laye s o he
p e ious model. Bo h o hese new laye s ea u e an inc eased dep h o 39
channels. Also, a he end o he encode , an addi ional dense laye is alloca ed
main aining he same con igu a ion o he h ee p eceding laye s. The decode , as
always, is he exac mi o . The h ee a chi ec u es desc ibed abo e con ain 982K,
5.78M, and 6.725M ainable pa ame e s, espec i ely. Fo each, di e en lea ning
a es ha e been es ed, and he inal con igu a ion is shown in Tables 4.4–4.6. The
aining esul s o he A-Con se a e shown in Fig. 4.24.
C21-C7-D512 Inpu H1 H2 H3 La en
Type - Con 3D Con 3D Dense Dense
Size 120,393 21x21x21 7x7x7 512 2
Con olu ion il e - (3x3x3)x1 (3x3x3)x1 - -
Op imize RMSP op, L (lea ning a e) = 0.0017, S ide = 1
All ac i a ions a e elu excep ou pu laye (sigmoid)
To al pa ame e s: 982k
Table 4.4: C21-C7-D512 ne wo k a chi ec u e (showing only encode o
simplici y).
2xC21-2xC7-3xD512 Inpu H1-H2 H3-H4 H5-H7 La en
Type - Con 3D Con 3D Dense Dense
Size 120,393 21x21x21 7x7x7 512 2
Con olu ion il e - (3x3x3)x1 (3x3x3)x1 - -
Op imize RMSP op, L = 0.0011, S ide = 1
All ac i a ions a e elu excep ou pu laye (sigmoid)
To al pa ame e s: 5.78M
Table 4.5: 2xC21-2xC7-3xD512 ne wo k a chi ec u e (showing only encode
o simplici y).
3xC21-3xC7-4xD512 Inpu H1-H2 H3 H4-H5 H6 H7-H10 La en
Type - Con 3D Con 3D Con 3D Con 3D Dense Dense
Size 120,393 21x21x21 21x21x21 7x7x7 7x7x7 512 2
Con olu ion il e - (3x3x3)x1 (3x3x3)x3 (3x3x3)x1 (3x3x3)x3 - -
Op imize RMSP op, L = 0.0009, S ide = 1
All ac i a ions a e elu excep ou pu laye (sigmoid)
To al pa ame e s: 6.72M
Table 4.6: 3xC21-3xC7-4xD512 ne wo k a chi ec u e (showing only encode o simplici y).
In he B-Dense g oup (Tables 4.7–4.9), he i s model (D2048-D512) bea s wo
hidden laye s ha a e densely connec ed o bo h he encode and he decode . The
i s hidden laye holds 2048 neu ons and he second one 512, which is 495.35M
120
0 10 20 30 40 50 60 70 80
epochs
0
500
1000
1500
2000
2500
3000
loss
_loss (C21-C7-D512)
_loss
_loss (2xC21-2xC7-3xD512)
_loss
_loss (3xC21-3xC7-4xD512)
_loss
Figu e 4.24: Bes aining esul s o A-Con scheme.
ainable pa ame e s. In he second model (4xD512), hese wo hidden laye s a e
eplaced by ou iden ical hidden laye s o 512 neu ons, hus educing he pa ame e
coun o 125.245M. Howe e , his alue may s ill be qui e high o he da ase a
hand. Finally, a hi d model (6xD112) is se up ha con ains up o six hidden laye s
o 112 neu ons each, bo h on he encode and decode . Howe e , his las model
cu s he o al pa ame e coun down o 27.215M, which is s ill a ema kable igu e.
The aining esul s o he B-Dense scheme a e shown in Fig. 4.25.
D2048-D512 Inpu H1 H2 La en
Type - Dense Dense Dense
Size 120,393 2048 512 2
Op imize RMSP op, L = 0.0012
All ac i a ions a e elu excep ou pu laye (sigmoid)
To al pa ame e s: 495.35M
Table 4.7: D2048-D512 ne wo k a chi ec u e (showing only encode o
simplici y).
The bes pe o ming a chi ec u es o each scheme a e 2xC21-2xC7-3xD512 and
6xD112. The i s one ea u es a o al o ou con olu ional hidden laye s and h ee
dense hidden laye s o bo h he encode and he decode . The second model is
composed o six dense laye s in be ween he inpu and he la en space and he
same laye s again in be ween he la en space and he ou pu laye o he
au oencode . The pe o mance o bo h models in e ms o alida ion loss is
ela i ely simila , as can be seen in Table 4.10 and Figs. 4.26,4.27. Howe e , he
121
Figu e 4.31: Geome y econs uc ed om la en space (blow-up). Model 6xD112.
pa icula , he pa ame e s ha ha e been mos limi ed a e wid h and leng h.
P e iously, hese wo dimensions we e ee o ake up he comple e size o he
can as, whe eas in he es ic ed da ase , hey do no exceed hal he leng h o
wid h o he can as. These wo s a egies ha e been es ed h ough wo
expe imen s. In he i s one, he da a se is inc eased and no hing else is al e ed,
and in he second one, he da a se is inc eased, and a limi o he a ia ion o he
pa ame ic augmen a ion me hod has been applied as explained abo e. The esul s
o hese expe imen s a e shown in Table 4.11 and Figs. 4.32–4.36. The da a show a
la ge educ ion in alida ion loss (50%) and a la en space wi h a e y clea pa e n
seg ega ion. I can also be obse ed ha he in e pola ion o geome y akes place
along a e y na ow passage in be ween he wo clus e s. A de ailed isualisa ion
o he ou pu geome y o he second case (modi ied and inc eased da ase ) is
shown in Figs. 4.37,4.38.
128
2xC21-2xC7-3x512 T aining loss Valida ion loss
Re e ence da ase 1029.86 1036.01
Da ase inc eased 1335.11 1357.23
Da ase inc eased and modi ied 464.34 506.75
Table 4.11: T aining esul s o 2 × C21-2 × C7-3 × 512 upon a ia ions o he da a se .
Figu e 4.32: La en space o 2xC21-2xC7-3xD512 model wi h he ‘inc eased da a se ’.
These las wo expe imen s we e an a emp o educe he econs uc ion e o
by p o iding a la ge da a se and limi ing he ange o a ia ions o he samples
ha a e gene a ed h ough pa ame ic augmen a ion. In Fig. 4.28, i can be
obse ed ha a la ge pa o he ansi ion g adien deals mainly wi h
accommoda ing a ia ions in size, a he han picking up mo phological o
opological ea u es, which a e cen al o his s udy. Thus, he mo i a ion behind
educing pa ame e a ia ion anges, such as hose applied o he wid h and leng h
o he samples, is o imp o e he accu acy o he ne wo k by elimina ing
unnecessa y in o ma ion ha leads o no ele an lea ning.
In he i s o hese wo expe imen s, he pa ame e s o he gene a ion o
samples h ough pa ame ic augmen a ion emained unchanged. Howe e , he
size o he da ase was mo e han doubled. In Fig. 4.32, he la en space
co esponding o his es e eals ha he model was o ally incapable o
129
Figu e 4.33: La en space o 2xC21-2xC7-3xD512 model wi h he ‘modi ied and inc eased da a se ’.
0 10 20 30 40 50
epochs
0
500
1000
1500
2000
2500
3000
loss
_loss (bes esul om p e ious expe imen )
_loss
_loss (da ase inc eased)
_loss
_loss (da ase inc eased and modi ied)
_loss
Figu e 4.34: Compa ison o aining esul s o 2xC21-2xC7-3xD512 model om he p e ious
expe imen wi h bo h he ‘inc eased da a se ’ and he ‘inc eased and modi ied da a se ’.
sepa a ing he wo ypes. The expe imen hus sugges s ha inc easing he numbe
o aining samples does no p o ide he ne wo k wi h be e lea ning p ospec s.
130
Figu e 4.35: Geome y econs uc ed om la en space. Model 2xC-2xC-3xD512 using he inc eased
and modi ied da a se .
This inding is a he in e es ing because he ini ial objec i e o using pa ame ic
augmen a ion was p ecisely o a o d he possibili y o gene a ing la ge da ase s as
equi ed by he complexi y o he p oblem a hand. Howe e , his esul shows
exac ly he opposi e: When he a ia ions achie ed h ough pa ame ic
augmen a ion a e oo b oad, he shea scope o hese may easily exceed he
hypo he ical bene i o p o iding mo e samples. In he second expe imen , he
pa ame e s ha guide hese a ia ions we e hea ily es ic ed in o de o p oduce
less he e ogenei y while s ill gene a ing he desi ed numbe o unique samples.
The esul s (Figs. 4.35,4.36) p o e ha he s a egy is e ec i e in educing he
alida ion loss app oxima ely a ound 50%, which is e y success ul. In addi ion,
ca ego ies a e clea ly sepa a ed a e encoding. Howe e , he esul an la en space
(Fig. 4.33) shows a ha d aul line be ween he wo aining ca ego ies. This
131
Figu e 4.36: Geome y econs uc ed om la en space (blow-up). Model 2xC-2xC-3xD512 using he
inc eased and modi ied da a se .
Figu e 4.37: Rende ed geome y econs uc ed om la en space. Model 2xC-2xC-3xD512 using he
inc eased and modi ied da a se .
132
Figu e 4.38: 3D p in ed geome y econs uc ed om la en space. Model 2xC-2xC-3xD512 using he
inc eased and modi ied da a se .
condi ion en ails ha in e pola ion o geome y may only happen in a e y na ow
a ea and ha ansi ions will no be able o display smoo h g adien s. In Fig. 4.35,
his e ec can be clea ly obse ed in he dis ibu ion o he gene a ed geome ies,
and he egion blow-up e ec i ely e eals ab up ansi ions along he aul line.
I is unclea a his s age he eason behind his allback in o unsa is ac o y
in e pola ion spaces, especially despi e he posi i e esul s in e ms o bo h
alida ion loss and spa ial seg ega ion in he la en space. Possible explana ions
may be connec ed o he pa icula geome ies selec ed o he expe imen s, in he
sense ha hey may no sha e common dis inc i e ea u es ha allow clean
in e pola ions. O pe haps, he ne wo k a chi ec u es implemen ed in his wo k
lack he abili y o cap u e global ea u es om one o bo h inpu ypes.
Finally, he e is ano he possible ac o ha should be men ioned, one ha
ouches upon he co e o he me hodology p esen ed he e and ha should be aken
in o conside a ion o u u e wo k. ML algo i hms a e essen ially op imisa ion
models. Mos o hem unc ion on he basis o he g adien descen , whe eby a
ele an local minimum o he loss unc ion may be ound. Howe e , loss unc ions
mus be con inuous and ac able and should no p esen equen o la ge a eas o
null de i a i e (pla eaus). I hese a eas a e p e alen in he unc ion, hen he
algo i hm may no know in which di ec ion o mo e when pu suing lowe loss
alues. I may assume ha i has al eady ouched bo om, o i may igge a
133
andom decision ega ding which di ec ion o ake, esul ing in high ola ili y
du ing he aining p ocess (as can be seen in Figs. 4.25,4.34) and low con e gence.
In ac , models ha did no easily con e ge ha e been p ominen ly p esen
h oughou much o he side wo k ca ied ou du ing he p esen s udy. The
al e na i e ep esen a ion o geome y p esen ed he e is based on a connec i i y
ec o o disc e e alues (0, 1). Fu he mo e, in his las expe imen , a ia ions
among he aining samples we e minimised o a oid an excessi e sp ead o
ea u es. This means ha many samples sha ed la ge se s o iden ical alues,
acili a ing he eme gence o la a eas in he loss unc ion. And whe e hose alues
we e di e en , a ansi ion pa e n was ha d o ind due o he disc e e na u e o
he ep esen a ion me hod chosen o app oach he p oblem. I may hus be
aluable when engaging in u he wo k o look in o some aluable esea ch ha is
cu en ly aking place o ackle deep lea ning p oblems in disc e e spaces. Wo ks
along he lines o [370,371] a emp o ind al e na i e ep esen a ions o hese
spaces ha smoo h ou he issues men ioned abo e. The adop ion o he me hods
p oposed in hese s udies may p o ide he answe s ha a e equi ed o imp o e
he esul s p esen ed in his wo k.
4.5.1 Conclusions
Due o he g owing in e na ional academic in e es in gene a i e machine lea ning
me hods and i s wide comme cial applica ions, he wo k low p esen ed in his case
s udy builds on he eme gence o a blooming ield. Al hough de eloped almos
en yea s ago, he use and use ulness o VAEs in he con ex o a chi ec u al design
emains mos ly unexplo ed.
The wo k p esen ed he e builds on he no ion o a connec i i y ec o ha is
used o ep esen 3D mesh-like geome ies, wi h he objec i e o acili a ing hei
p ocessing by neu al ne wo ks in gene al and VAEs in pa icula . This
ep esen a ion was explo ed in [358], whe e a da a se comp ising wo building
ypes was gene a ed h ough noise- and displacemen -based enhancemen . The
esul s sugges ed on he one hand ha noise did no help he ne wo k in
iden i ying pa e ns. And, on he o he hand, ha he displacemen app oach was
always p one o o e i ing, because he la ge he displacemen space, he mo e
he numbe o ainable pa ame e s g ew. In his con ex , he main objec i e o he
p esen wo k has been o explo e he sui abili y o an al e na i e augmen a ion
me hod o assis in he gene a ion o no el geome ies wi h a VAE.
This al e na i e me hod, pa ame ic augmen a ion, has allowed e y la ge da a
se s o be c ea ed wi hou he need o inc ease he size o he 3D-can as (and
consequen ly he size o he inpu laye and o al numbe o ainable pa ame e s),
134
as was he case in he p e ious app oach. Addi ionally, pa ame ic augmen a ion is
pa icula ly e icien o inc easing da a se s o 3D geome ies wi hin he ield o
a chi ec u al geome y – especially when esembling building ypes, due o he
disc e e ye obse able cha ac e is ics o each sample, as cons i uen o each ype.
The esul s p esen ed show ha he me hod was indeed success ul in p e en ing
he o iginal o e i ing p oblem. Consequen ly, he au oencode was success ul in
econs uc ing he geome ies o he da a se . Howe e , he augmen a ion me hod
has c ea ed ano he se o p oblems ha ha e challenged he pe o mance o he
VAE.
Fi s ly, esul s show ha he ea u e sp ead p oduced h ough pa ame ic
augmen a ion can o e whelm he ne wo k and can hinde i s abili y o ex ac
hose ea u es. This was made appa en when an inc ease in he size o he da ase
wo sened he econs uc ion e o a he han imp o ing i . This limi a ion blocked
he possibili y o expanding he da ase o imp o e he de ini ion o he geome ies
ha a e gene a ed by sampling om he la en space. Thus, al hough he e we e
smoo h ansi ions ac oss he wo ypes p esen in he esul ing geome ies, hese
emained qui e blu y. Secondly, when a emp ing o coun e he la e issue by
limi ing he ange o he pa ame e s in ol ed in building up he aining se , i was
ound ha despi e being e ec i e in u he lowe ing he econs uc ion e o ,
ansi ions ac oss ypes had been d as ically educed.
An impo an akeaway om he expe imen a ion is ha he e seems o be a
mo e undamen al p oblem unde lying he di icul ies aced by he VAE. As
discussed in he p e ious sec ion, he ep esen a ion based on a connec i i y ec o
as implemen ed in his s udy c ea es a ough landscape o na iga e wi h
op imisa ion algo i hms. This is mainly due o he disc e e and spa se na u e o he
da a se . Po en ial a enues o esea ch ha may shed ligh on o his p oblem ouch
upon ans o ma ion echniques om disc e e spaces in o con inuous ones. Some
o hese ha e been ea ma ked o u u e wo k, as hey a e cu en ly being pu sued
by se e al au ho s. Despi e he di icul ies, he inal esul s show pa ial success in
gene a ing new geome ies om he la en space ha sha e a mix o ea u es om
he wo ypes p esen in he aining se , which was he ini ial objec i e o he
esea ch. The quali y o hese new samples achie es a ce ain deg ee o
in e pola ion as can be obse ed in Figs. 4.37,4.38, al hough he de ini ion o he
esul ing geome ies may s ill be imp o ed.
Aside om he de ini ion o he esul s, he main con ibu ion o his wo k has
been o explo e an al e na i e a enue o he pa ame ic gene a ion o la ge
da ase s o 3D geome ies, showcasing i s p oblems and limi a ions in he con ex
o neu al ne wo ks and VAEs and poin ing ou po en ial solu ions o u u e wo k.
135
In gene al, he p oposed wo k low challenges designe s o acqui e a c i ical
pe spec i e o he impac and po en ial o AI in ou socie y and design p ac ices.
Gene a i e neu al ne wo k models ha e a la ge po en ial o ede ine how a chi ec s
and designe s wo k wi h a chi ec u al p eceden s, ha is, o use hem di ec ly as
da a o design gene a ion. This case s udy aims o show he po en ial o such
echniques and open a discussion abou he u u e o machine lea ning in he
con ex o geome y gene a ion o he a chi ec u al design indus y.
136
5. Concep ep esen a ion and u ban space: he case o
eal es a e ma ke s
The p e ious chap e has explo ed he la es gene a i e me hods wi hin he
connec ionis pa adigm. The applica ion o gene a i e models o he ield o
Design has highligh ed he impo ance o a sui able ep esen a ion s a egy o
h ee-dimensional geome ic da a. Speci ically, i has been shown ha a chi ec u al
a i ac s can scale up he size o he neu al inpu laye s e y quickly; o he poin
whe e e en oday’s mos powe ul ha dwa e is ende ed incapable o dealing wi h
such amoun s o aining pa ame e s. The e o e, al e na i e da a ep esen a ion
s a egies a e necessa y and a e cu en ly being explo ed. Addi ionally, neu al
ne wo k models ha e ce ain limi a ions when dealing wi h he e ogeneous da a.
The inpu laye s o hese models a e no adap able du ing aining, meaning ha
hey mus handle inpu s o he exac same size and s uc u e h oughou . This is
ine icien , as seen in he p e ious case s udy, because he ne wo k is o ced o
accoun o an inpu laye size ha i s all he examples in he aining da a. Thus,
i is ele an o explo e o he me hods ha may o e in e es ing al e na i es o
handling la ge-scale 3D da a. This is especially pe inen in he case o e en
la ge -scale s udies, i.e. u ban analysis. As in he p e ious U ban In e mezzo, his
chap e also in oduces and exempli ies h ough an u ban analysis p oblem
(u ili as), a echnique ha will be p esen ed in mo e de ail la e : Fo mal Concep
Analysis (FCA). The heo y and ools p o ided by FCA allow o a di e en
app oach o he ep esen a ion o da a ha ope a es on a highe symbolic le el.
Thus, a good pa o he hea y li ing equi ed by neu al models ha deal wi h aw
da a is alle ia ed. O cou se, his comes wi h i s own limi a ions, which will be
discussed in he nex chap e . Finally, his case s udy using FCA allows opening
he pe spec i e and con as ing he con e sa ion on concep ual knowledge wi h
he ecen incu sion in he connec ionis domain.
5.1. In oduc ion
Today, u ban ecosys ems p oduce da a ha enable one o manage, compa e, and
sha e huge amoun s o in o ma ion abou he ci y. Acco ding o i s na u e, u ban
da a can be g ouped in o di e en se s o in o ma ion laye s, which, as o he
in o ma ion eposi o ies and sys ems, a e p one o p oblema ic issues such as
noise, inconsis encies, and ambigui y.
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