Bayesian Modelling of Nuclear Fusion
Experiments
vorgelegt von
B.Sc.
Sehyun Kwak
ORCID: 0000-0001-7874-7575
an der Fakultät II – Mathematik und Naturwissenschaften
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
— Dr. rer. nat. —
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr. Holger Stark
Gutachter: Prof. Dr. Dieter Breitschwerdt
Gutachter: Prof. Dr. Robert Wolf
Gutachter: Prof. Young-chul Ghim
Tag der wissenschaftlichen Aussprache: 04.11.2020
Berlin 2020
As far as the laws of mathematics refer to reality,
they are not certain, as far as they are certain, they
do not refer to reality.
Albert Einstein, 1921
Abstract
Bayesian probability theory as a general framework for scientific modelling and
inference is introduced and applied to nuclear fusion experiments in order to
provide consistent inference solutions given multiple heterogeneous data sets.
Fusion plasmas are complex physical systems, in which charged particles are
confined by the electromagnetic force. The physics parameters of the plasmas
involve various independent measurements from sophisticated scientific instru-
ments. Owing to the complexity of the experiments and the fusion plasmas,
so far, no physics model can predict major physical phenomena, like trans-
port, sufficiently well. Hence, generic, non-parametric Gaussian processes are
used to model physics parameters such as plasma current density and pres-
sure. Multiple predictive models of scientific instruments have been developed
individually, and they have been combined into a joint model with Gaussian
process priors in order to perform robust and consistent inference. The joint
model provides the joint posterior probability distribution of the physics para-
meters, hyperparameters and other unknown parameters, such as calibration
factors. This thesis theoretically and experimentally shows that the joint pos-
terior distribution intrinsically embodies Bayesian Occam’s razor. Therefore, by
exploring the joint posterior distribution, inference solutions can be found with op-
timal values of all the model parameters, based on the principle of Occam’s razor.
In other words, we can apply Bayesian Occam’s razor to real-world problems
without calculation of the model evidence, typically requiring marginalisation
over a high-dimensional parameter space, which is one of the major obstacles to
Bayesian model selection. Based on this foundation, several applications have
been developed for consistent inference of the physics parameters of the fusion
plasmas at two major fusion experiments, the Joint European Torus (JET) and
Wendelstein
7-X
(
W7-X
). The first application has been developed by modelling
emission spectra and relevant atomic physics for the lithium beam emission
spectroscopy system at JET to provide the edge plasma electron density pro-
files and their posterior uncertainties. Additionally, interferometers, Thomson
v
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