GENCI Demande d’A ibu ion de Ressou ces In o ma iques
Desc ip ion scien i ique du p oje
Ti e du p oje : Towa ds hyb id me a-
modelling ea hquake scena ios : imp o ing high- ideli y nume ical simula ion
wi h machine lea ning echniques.
Num´e o du p oje DARI 1: A0060410444
Responsable scien i ique 2(nom, p ´enom) : LOPEZ-CABALLERO
Fe nando (Maˆı e de Con ´e ence/LRU) - e nando.lopez-caballe o@cen alesupelec.
Labo a oi e : Cen aleSup´elec - Labo a oi e MSSMa UMR CNRS
8579
Nomb e d’heu es demand´ees (Cpu mono-p ocesseu ) su le p o-
je :
CINES BULL noeuds ins Occigen : 2.500.000 heu es scalai es
1 R´esum´e
The objec i e o his p ojec is o p edic he dynamic beha iou o s a-
egical s uc u es (such as nuclea powe plan s) and o assess he seismic
esponse o la ge seismic-p one u ban a eas, a he occu ence o ex eme
g ound shaking e en s. To his end, we ha e ecen ly de eloped an e icien
mul i- ool compu a ional pla o m, capable o simula ing b oad-band non-
linea seismic wa e p opaga ion in highly he e ogeneous media, om he
aul o he abo eg ound s uc u es (i.e. a a egional scale). The co e o he
pla o m is ep esen ed by SEM3D, a Spec al Elemen (SE) Me hod code ai-
lo ed o sol e 3-D wa e p opaga ion in aniso opic, andomly he e ogeneous
and non-linea geo-ma e ials. The pla o m e icien ly handles he p esence
o complex su ace opog aphy, coas lines and ba hyme y, 3-D geological
con igu a ions along wi h la ge aul discon inui ies [Ga i˙e ˙al˙2017a,21,
24,25,26]. The wa e-p opaga ion code has p e iously shown e y good sca-
labili y in mesh ea u ed by millions o hexahed al elemen s. Fo ins ance, we
s udied he seismic esponse o he Kashiwazaki-Ka iwa Nuclea Powe Plan
(KKNPP), du ing he MW6.6 2007 Niiga a ea hquake (cen al wes -coas o
Japan) eaching a maximum equency max o 7 Hz, in a compu a ional do-
main o 60 km ×60 km×60 km, wi h a minimum g id size o 200 m ×200 m ×
200 m, wi h minimal shea wa e eloci y o 700 m/s [25]. Simila ea hquake
1. Uniquemen en cas de demande de p olonga ion d’un p oje exis an .
2. Le esponsable se cha ge du sui i du p oje e ou ni un bilan en in d’ann´ee.
1
scena ios a e cu en ly being un o he A gos oli si e (a Eu opean es si e,
whe e a as geophysical and ec onic su ey a e cu en ly ca ied ou ), wi-
hin he amewo k o he ongoing A0040410444 call. The pe o mances o
SEM3D ha e been checked wi hin his ongoing p ojec (see ac i i y epo ) :
o he A gos oli es case, we managed o pe o m ou la ges physics-based
high- ideli y nume ical simula ion o a main shock ea hquake scena io, e-
liable up o a maximum equency o 10 Hz, in he so es pa o he domain
(i.e. whe e sho e wa e leng hs mus be co ec ly disc e ized).
Howe e , eal case s udies a e ea u ed by e y so soil deposi s ( ypically
eaching alues o 200 m/s), equi ing highe spa ial esolu ion o he same
maximum equency p opaga ed ( he A gos oli es case is ea u ed by a mi-
nimum shea -wa e eloci y o 650 m/s). Fu he mo e, he modal esponse
o igid s uc u es ( o ins ance he eac o buildings) shi s owa ds highe
equencies (≥10 Hz), ha should be exci ed by b oad-band syn he ic inpu
mo ion ( o ins ance, o a Soil-S uc u e In e ac ion model a he si e scale).
Finally, he possibili y o modelling he he e ogeneous spa ial luc ua ions
and unce ain y o he inpu pa ame e s in a non-linea wa e p opaga ion
con ex (due o he de elopmen o a e y e icien andom ield gene a o
o e la ge domains, coupled wi h SEM3D), pe mi s he modelling o complex
sca e ing e ec s aking place a highe equencies (i.e. highe spa ial eso-
lu ions) and leads o explo e di e en ealiza ions o he same ea hquake
scena io.
The e o e, we conside in his p ojec an ex ension o he men ioned ana-
lyses (see, o ins ance, [25,26,27]). We ha e a leas h ee es s cases in
ou disposal : he egion su ounding he KKNPP, he A gos oli basin and
he Vol i basin (ano he expe imen al si e in G eece). This achie emen will
be exploi ed o imp o e p obabilis ic ulne abili y assessmen , using unce -
ain y p opaga ion echniques (cons uc ion o me a-model simula ions and
agili y cu es). As a ma e o ac , high- ideli y ea hquake simula ions can
be exploi ed o ei he cons uc b and-new si e-speci ic da abases including
a g ea numbe o syn he ic g ound mo ions, ei he o in eg a e exis ing e-
co ding da abases, o be exploi ed o se e al pu poses. In o he wo ds, he
esul s o he se o cumbe some simula ions o eseen in his p ojec will be
a sui able basis o su oga e modelling (pe o med ex e nally, in a pos e-
io phase, by applying, o ins ance, machine lea ning echniques such as
ANN2BB [29]), so as o educe he compu a ion ime associa ed keeping an
accu a e p edic ion. Howe e , in doing so, he expe imen al design (ED) is
cons uc ed by SEM3D analyses.
2
2 P ´esen a ion g´en´e ale
Fo a long ime, geophysicis s ha e concen a ed on wa e p opaga ion
in simpli ied geological media (e.g. conside ing he Ea h’s c us as sub-
ho izon ally laye ed isco-elas ic hal -space) neglec ing c ucial issues, such
as :
— he he e ogenei ies in he Ea h’s c us (a egional and si e scale)
— he non-linea i y o shallow soil deposi s
— he su ace opog aphy
— solid- luid in e ac ion (coas lines, ba hyme y e c)
Al hough he men ioned nume ical models we e capable o ep oducing ea-
sonably well he P, S o Rayleigh wa es a i al imes and he main e lec-
ions wi hin he Ea h’s c us , hey we e gene ally limi ed o he e y low-
equency pa o he adia ed spec um.
Mo eo e , e y a e a e he examples o a con inuous aul - o-s uc u e in e -
ac ion s udies. The mos eliable and e icien me hod was p oposed by Bielak
e al. [8], called he Domain Reduc ion Me hod. I consis s in o a wo-s ep
analysis, declined as ollows : (i) egional scale wa e-p opaga ion in simpli ied
geological medium ( ypically he deep isco-elas ic s a i ied Ea h’s c us ),
no including he non-linea si e-e ec s ; (ii) a second un o he analysis on
a smalle domain (e en ually adding he s uc u e) delimi ed by an a i icial
bounda y a which equi alen ine ial o ces and ee- ield eloci ies, ob ai-
ned in he p eceden s ep, a e applied. Quinay e al. [13] applied his me hod
o s udy he s uc u al esponse o he Kashiwazaki-Ka iwa Nuclea Powe
Plan (KKNPP) in a aul - o-s uc u e amewo k, up o 1 Hz.
Those aspec s clashes wi h he need o b oad-band ealis ic syn he ics o
inpu in o ealis ic s uc u al models : he ansien dynamics o abo e-
g ound s uc u es (e en ually wi h soil-s uc u e in e ac ion a he si e scale)
has been adi ionally s udied sepa a ely, by employing selec ed spec um-
compa ible eco dings. In any case, he seismic design o c i ical s uc u es
equi es e ined analyses p o iding syn he ic g ound mo ion ime-his o ies
eliable a highe equencies and ep oducing complex phenomena such as
he coda in he seismic signals [2], he di ec i i y and he incohe ence o he
wa e mo ion nea -sou ce [24], he non-linea si e e ec s [20].
The e e inc easing a ailabili y o compu e powe pa es he way o de e -
minis ic explo a ion o he scena ios space, compa ibly wi h he deg ee o
knowledge o ocal issues, such as :
1. he 3-D geological s uc u e o he Ea h’s c us
2. he geomechanical p ope ies o soil deposi s and deep bed ock
3
3. he su ace mo phology ( opog aphy, ba hyme y, coas lines)
4. he cha ac e is ics o he ac i e aul s ( ec onic con ex , slip pa ches,
ocal mechanisms)
The le el o unce ain y ela ed o his piece o in o ma ion, con ol ed oge-
he wi h he nume ical dispe sion, de e mines i s p edic i e ideli y o such
physics-based analyses. Resea che s a e ying o add ess hose issues, mainly
h ough ull-wa e o m in e sion [16,22], noise co ela ions [Book˙Fouque˙e ˙al˙2008˙Wa e˙P opaga ion˙Random˙Laye ed],
p obabilis ic models o he luc ua ions [6,7], complex heological models.
In his p ojec , ins ead, we y o employ he e icien mul i- ool pla o m
de eloped so a o ep oduce nume ically hose obse a ions, when consi-
de ing high esolu ion wa e p opaga ion p oblem using con o mal hexahe-
d a, which a e necessa y o he widely used spec al ini e elemen me-
hod [Koma i sch˙T omp˙I˙2002,5,9]. Mo eo e , we aim a calib a ing
hose models wi h he s uc u al dynamics coun e pa [13], o o wa d ul-
ne abili y assessmen . He e, high esolu ion means meshes con aining bil-
lions o elemen s [11,14,15]. Pe o ming wa e p opaga ion in such meshes
becomes a possibili y h ough he unp eceden ed de elopmen o powe ul
compu a ional esou ces and scalable pa allel sol e s. Howe e , cons uc ing
e icien ly such disc e iza ions and unning he simula ions on such meshes is
no an easy ask. Recen ly some esea ch g oups ha e sha e ed he ba ie
o unning analyses on e y la ge meshes, exhaus ing all esou ces on e y
la ge machines all o e he wo ld. An imp essi e esul was ob ained by a
Chinese esea ch g oup, who un an non-linea ea hquake simula ion o e a
con inen al 320 km by 312 km by 40 km egion, up o 18 Hz [19]. The use
o oc ees has made possible a high deg ee o scalabili y in mesh gene a ion
using up o 220.000 co es [11].
To ackle he men ioned obs acles, ecen ly, we ha e de eloped a se ies o
compu a ional ools ha help in cons uc ing la ge scale nume ical scena io
o an ea hquake e en , namely :
— a nume ical echnique ha allows o gene a e con o mal hexahed al
meshes using an oc ee-based me hod simila o [12] ;
— an e icien andom ield gene a o o e la ge compu a ional domains [28],
based on a ully pa allelized e sion o he spec al ep esen a ion ech-
nique [4] ;
— a pa allel non-linea wa e-p opaga ion sol e based on he spec al
elemen me hod and coupled wi h he andom ield gene a o [21].
The pa allel oc ee-based mesh gene a o is able o ea imme sed geome-
ies wi h high scalabili y in execu ions. I was es ed up o 6561 p ocessing
co es. The mesh can be non-con o mal, composed exclusi ely by hexahe-
d al elemen s, o i can be made con o mal using e ahed al elemen s. Non-
4
con o ming meshes ha e hanging nodes, (i.e. nodes loca ed inside edges o
aces), which es ic s i s use o nume ical me hods ha p o ide suppo o
his ype o nodal in e pola ion. In pa icula , e icien pa allel implemen-
a ion o he SE Me hod (SEM) equi es he use o con o mal hexahed a.
Owing o he SEM spec al con e gence, highe esolu ion is ob ained by p-
e inemen (i.e. by inc easing he polynomial o de ) a he han by inc easing
he numbe o linea elemen s (common p ac ice in Fini e Di e ence/Elemen
schemes).
The andom ield gene a o employs he sum o a se ies o Nϕcosines wi h
andom phases/ampli udes [4], sampled o e ine egula g ids [21]. The
Fas Fou ie T ans o m can be used o b ing he complexi y o his gene-
a ion me hod o O(Nϕlog Nϕ). The ield is hen e-in e pola ed o e he
no uni o mly space-dis ibu ed SE g id ( ea u ed by 5 o 10 Gauss-Loba o-
Legend e poin s pe dimension). When dealing wi h la ge domains, he scala-
bili y issue is sol ed by gene a ing smalle independen ealiza ions, suppo -
ed on o e lapping subdomains (in a dis ibu ed memo y pa allel scheme),
and hen ecomposed oge he in o he ull domain.
Finally, he non-linea wa e-p opaga ion sol e exploi s he high esolu ion
o he spec al elemen me hod wi h e icien explici algo i hm o in eg a e
non-linea heology ep esen ing he non-linea cyclic beha iou o soils.
3 M´e hode
3.1 M´e hode num´e ique
The compu a ional pla o m we a e in ended o es in his p ojec ba es
upon h ee nume ical codes :
— SEM3D : an e icien Spec al Elemen code ailo ed o wa e-p opaga ion
in non-linea he e ogeneous geo-ma e ials a he egional and con i-
nen al scales [21] ;
— HexMesh 3: a scalable oc ee-based mesh gene a ion code ;
— andomField 4: a scalable andom ield gene a o o e la ge compu-
a ional domains, based on he spec al gene a ion echnique [3].
The i s code is he cen e o ou a en ion in his p ojec and has al eady
un e icien ly on la ge scale machines, ep oducing eal ea hquake scena ios
wi h high accu acy. The second and hi d codes a e used in conjunc ion wi h
he spec al elemen code, so o mesh co ec ly he complex mo phology o
he Ea h’s c us s uc u e and i s heology wi h na u al spa ial luc ua ions.
3. h ps://gi hub.com/jcama a/HexMesh.gi
4. h ps://gi hub.com/co e eau/ andomField.gi
5
Non-linea wa e p opaga ion : SEM3D
We de elop SEM3D [18] join ly by he Ins i u de Physique du Globe
de Pa is, CEA and Cen aleSup´elec, mainly o applica ions in geophysics,
wi h he aim o conside ing ealis ic 3-D complex geo-s uc u es. I is w i -
en in Fo an 95, and uses MPI. The I/O is pe o med using pa allel HDF5
lib a ies. The meshes a e non-s uc u ed and composed o con o mal hexa-
hed a by employing METIS 5lib a y. The disc e iza ion in space is based on
spec al elemen s in space and an explici scheme in ime (bo h o elas ic
and non-linea case). The spec al elemen me hod is a a ian o he i-
ni e elemen me hods which uses high-o de Lag ange polynomials on Gauss-
Loba o-Legend e (GLL) poin s. The co esponding quad a u e ensu es ha
he mass ma ix is diagonal. Hence, in e sion o he mass ma ix a each
ime s eps is no cos ly and e y sho ime s eps, imposed by he explici
scheme, a e no an issue. The code was es ed on se e al clus e s, including
Cu ie (by CEA) and he M´esocen e de Cen aleSup´elec and ENS Pa is Sa-
clay (SGI ICE X) and GENCI Occigen (c20150447417 and he ongoing A4
alloca ion p ojec A0040410444). Mo eo e , i has been un on he 64-nodes
Bi-Op e on clus e o Se ice de Calcul Pa all`ele de l’Ins i u de Physique du
Globe de Pa is (a model wi h 25 millions deg ees o eedom, unning o e
128 co es). A p e ious e sion o he code (less e icien in e ms o pa alle-
lism [23]) was es ed on Jade, in a p e ious GENCI p ojec (c2010046485).
On hese occasions, he weak scalabili y o he spec al elemen sol e has
been demons a ed. Finally, i should be no ed ha a code wi h simila ea-
u es and s uc u e (al hough de eloped by a comple ely di e en eam) was
po ed on he la ges clus e s a ailable (see o example [9], 15 yea s back).
An example o weak scalabili y cu e ob ained o SEM3D is shown in Fi-
gu e 1. SEM3D has been un o e mo e han 4096 co es. Mo eo e , gi en
he expe ience o alloca ion A4 (wi h mid- e m co ec ion), a compa ison
be ween SEM3D pe o mances ob ained on FUSION (clus e o M´esocen e
Moulon) and OCCIGEN we e compa ed be ween each o he , o check ou
es ima ions in e ms o equi ed CPU-hou s. The nume ical models o he
Niiga a ea hquake (scena io 1) and A gos oli basin (scena io 2) we e ex-
ploi ed. Ten simula ions a e he ea e compa ed : F1-F5, un on FUSION,
O1-O5, un on OCCIGEN (see he speci ics in Table 1). Fig. 2shows he
pe o mances ob ained, compa ed o he o iginal (CP) and co ec ed-blind
(BP) p edic ion (made be o e alloca ion A4). Fi s and o emos , we no iced
a e y good ag eemen be ween he co ec ed p edic ion CP and F1 and BP
and F4, which jus i ies ou p edic ion made on FUSION.
Howe e , we needed some p elimina y i e a ions (co esponding o simula-
5. h p://gla os.d c.umn.edu/gkhome/ iews/me is
6
Figu e 1 – Weak scalabili y cu es ob ained o SEM3D, exp essed as numbe o ime
a e o mesh elemen s p ocessed a ying he numbe o MPI p ocess employed. In
blue, he linea scalabili y cu e ep esen s he ideal op imum esul (pe ec ly linea
scalabili y). G een and ed lines po ay he wo s and a e age pe o mances ins ead.
ions O1-O3) o eplica e he same pe o mances ob ained on FUSION (in
e ms o CPU- ime). Speci ically, p elimina y simula ions O1-O3 (pe o med
wi hou he CINES suppo , be o e he mid- e m alloca ion) showed a in-
c eased compu a ion bu den (exp essed as CP U / EQK ). Fo ins ance, O2 and
F4 ep esen s he same simula ion, al hough we ob ained a CPU- ime pe se-
cond eal ime simula ion CP U / EQ [h/s] o 1.82×103h/s o FUSION and
3.49×104h/s o OCCIGEN espec i ely. I e a ion O4 was pe o med hanks
o he CINES suppo : he same pe o mances we e ob ained o FUSION
and OCCIGEN on he same es case. This i e a ion alida es SEM3D po -
abili y on OCCIGEN and allowed us o ob ain mid- e m ex a hou alloca-
ions. In he ollowing, we ansi ioned owa ds a highe numbe o DOFs by
imp o ing he nume ical model o A gos oli (including he new code ea u e
ep esen ed by he ex ended aul seismic sou ce) p e iously un on FUSION
(F5). On OCCIGEN, he same nume ical model was conside ed (called O5),
i s accu acy being inc eased by p− e inemen , i.e. by inc easing wo imes
he GLL poin s pe edge ( esul ing in 10×10×10 GLL poin s pe elemen ),
o a o al ≈13.48 ·109. Expec ed pe o mances we e a ained (quasi-linea
scalabili y) and we success ully passed he limi o 1010 DOFs (ne e be o e
achie ed on FUSION), hanks o he possibili y o unning jobs o e >720
CPU - co es (cu en limi a ion o FUSION).
7
10 810 910 10 10 11
DOFs [1]
10 1
10 2
10 3
10 4
CP U / EQK [h/s]
F=Fusion; O=Occigen
O1
O2
F1
F2
F3
F4
F5
Figu e 2 – CPU- ime pe eal ea h-
quake simula ion CP U / EQK , o di -
e en DOF numbe s. BP and CP co -
espond o he blind and co ec ed-
blind p edic ions espec i ely (see mid-
e m alloca ion).
NEL NGLL NMP I
F1 2×1065 648
F2 - 7 648
F3 - 10 648
F4 18×1065 648
F5 4.5×1065216
O1 - 5 4800
O2 - 5 648
O3 - 7 648
O4 - 5 4800
O5 4.5×10654000
CP 2×1065 216
BP 18×1065 648
Table 1 – Ea hquake nume ical mo-
del. NE: numbe o hexaed ael ele-
men s (8-nodes) ; NGLL : numbe o
GLL poin s pe elemen ) ; NMP I :
numbe o CPU co es.
Oc ee-based Mesh Gene a ion : HexMesh
Oc ees a e hie a chical da a s uc u es ha allows he decomposi ion a
h ee-dimensional space in egula cubes, called oc an s. The ini ial oc an
no mally su ounds all he inpu domain and is di ided in 8 equally spaced
cubes - he child oc an s. Each o hese child en could be subdi ided again,
in a ecu si e p ocess ha is usually limi ed by some c i e ia (i.e. maximum
numbe o subdi isions, minimum oc an size). An oc ee can be implemen ed
by a ee s uc u e o by a linea oc ee, whe e only oc an s wi h no child en
a e s o ed. In his las ep esen a ion, as also known by linea oc ee, each
lea is s o ed as a unique in ege - called loca ional code - which iden i ies
i s posi ion and dep h le el in he ee. Among he bene i s o linea oc ees
is he implici ep esen a ion o in e media y oc an s (non-lea es), making i
memo y e icien , and be e pe o mance on sequen ial access. Addi ionally,
by no making use o memo y poin e s, pa allel implemen a ion o he linea
oc ee has a lowe o e head in in e p ocess communica ion (in compa ison
o o he ee s uc u es [10]). We ha e implemen ed a se o algo i hms ha
add ess he special needs o pa allel oc ee meshing. These algo i hms a e :
(i) Oc ee ini ializa ion algo i hm ha gua an ees ha all p ocesses ha e a
leas one piece o he linea oc ee. (ii) Re inemen algo i hm ha decompose
8
he oc an s acco ding o some e inemen c i e ion (i.e. maximum size o
posi ion ela i e o he geome y bounda ies), and 2 :1 balancing algo i hm
ha ensu e ha no neighbo oc an s di e en ia e in mo e han one le el [10].
This las algo i hm is impo an because a balanced oc ee esul s in mo e
smoo h ansi ions be ween elemen s, a ea u e ha has a di ec in luence
on he inal mesh quali y. I also gua an ees ha he esul ing mesh will
no ha e mo e han one hanging node o each edge o ace, educing he
complexi y o con o ming mesh p ocess. The esul ing code has been w i en
in plain C and makes use o MPI only. The code uns on any s anda d
clus e . A p e ious e sion o he code (gene a ing non-con o mal hexahed a
and con o mal e ahed a meshes) has been es ed a S ampede Dell clus e
(a TACC) and on a SGI ICE 8400 and on a O acle clus e in B azil. Table 2
p esen s a weak scalabili y es pe o med on he mesh o he Ke alonia egion
(G eece). The communica ion ime (las column) a ains a ai ly cons an
pe cen age o he o al ime. The code has un o e 6561 MPI co es.
Co es Le els Nodes Elemen s Time (s) Comm(%)
81 7 85,602,744 83,102,679 12.061 21 %
243 8 769,790,232 747,937,476 32.994 20 %
729 9 6,926,153,724 6,731,438,013 105.188 25 %
6561 10 62,330,385,168 60,583,119,264 123.066 29 %
Table 2 – Weak scaling o he mesh gene a ion o he Ke alonia egion in G eece.
Co es : numbe o MPI co es ; Le els : oc ee e inemen le el ; Nodes : numbe o
mesh nodes ; Elemen s : numbe o mesh elemen s ; Time : gene a ion ime ; Comm :
pe cen age o he o al elapsed ime o communica ion ope a ion.
Random Field Gene a ion : andomFields
The he e ogeneous p ope ies o he Ea h’s c us a e included in ou
modelling s a egy o la ge scale ea hquake scena ios. In his con ex , by
la ge we e e o a domain size Lmuch la ge han bo h he co ela ion
leng h ℓC(o some cha ac e is ic size o he luc ua ion) and he disc e i-
za ion s ep h. I is he e o e ad an ageous o ep esen hose luc ua ions
a scala andom ields ( o ins ance, ep esen ing he spa ial dis ibu ion o
he shea -modulus). Those la ge andom ields can be e ec i ely sampled
o e a coa se g id (wi h a s ep size ele an o he co ela ion leng h) and
hen in e pola ed on o he mesh o in e es (p o ided by he GLL (Gauss-
Loba o-Legend e) g id used in SEM3D). I he disc e iza ion s ep is much
la ge han he co ela ion leng h, he sampling becomes simple and nu-
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