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@PHDTHESIS{Liang:980351,
author = {Liang, Zhouji},
othercontributors = {Wellmann, Jan Florian and Ghattas, Omar},
title = {{D}erivative-informed {B}ayesian inference for trainable
geological modeling - in modern machine-learning framework},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2024-02206},
pages = {1 Online-Ressource : Illustrationen},
year = {2023},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University 2024; Dissertation, RWTH Aachen University, 2023},
abstract = {Earth’s subsurface remains the most vital source of
energy and minerals for humankind. However, these subsurface
resources cannot be extracted without a comprehensive
understanding of what lies beneath our feet. Geoscientists
have dedicated significant efforts characterizing the
subsurface to guide resource development decisions and have
increasingly relied on computer modeling software. A 3D
structural geological model serves as such a tool that
encapsulates the knowledge of geoscientists and provides an
efficient visualization, communication, and advanced
analysis. Ensuring a faithful representation of the
subsurface is a crucial task for the geological model, both
from the financial point of view and for safety reasons.
Conventionally, a single model is developed based on the
modeler’s best knowledge. Yet, any criteria the model was
based on beyond our actual observation is subject to certain
uncertainties, for example, the input data, the
interpolation, and the missing knowledge. A good
quantification of these uncertainties is fundamental for the
success of the application of geological models. The
Bayesian framework offers a systematic approach to
simultaneously consider the uncertainties in the prior
knowledge and additional observations within the likelihood
function. The inferred probability with the consideration of
additional observations is referred to as the posterior
probability. This inference problem often cannot be solved
analytically. Evaluating the posterior distribution is
equivalent to the exploration of the posterior space and is
often solved using Markov Chain Monte Carlo (MCMC) methods.
In the geosciences, geophysical data is widely used to
characterize the subsurface through collection of
observations of physical signals. The accumulated scientific
expertise and collected geophysical surveys make geophysical
data an attractive candidate for uncertainty quantification.
However, integrating geophysical observations in the
Bayesian Framework is challenging due to difficulties in
calculating chained derivatives of geological followed by
geophysical simulations. This thesis presents an end-to-end
methodology to solve the problem of integrating potential
field data, specifically gravity, into the Bayesian
inference framework by leveraging advanced
derivative-informed inference methods, implemented in a
Machine Learning framework - TensorFlow. First, methods are
introduced to simulate gravity data from a geological model
using the implicit modeling method. The proposed kernel
methods for gravity simulation take advantage of the value
that can be queried at any position in space based on the
implicit modeling methods to achieve a more efficient
gravity calculation. In addition, a refinement strategy is
proposed to achieve better accuracy in the probabilistic
modeling framework. Then, methods to create trainable
geological models are introduced. The proposed methods
introduce a smooth slope function to bridge derivative
discontinuities between geological modeling and gravity
simulation. The proposed method enables meaningful
derivatives to be calculated from a geological inversion to
allow the application of advanced inference methods. A
visualization method using the order-reduction technique is
adopted to visualize the trainable posterior space. Finally,
by combining the introduced gravity simulation methods and
trainable geological modeling technique, this study is the
first attempt to adopt advanced inference methods, including
the Hessian-informed MCMC (generalized preconditioned
Crank-Nicolson, gpCN) and gradient-informed variational
method (Stein Variational Gradient Descent, SVGD) to the
application of probabilistic geological modeling. The
approach to efficiently evaluate Hessian information based
on the trainable geological concept is introduced. The
proposed methodology using gpCN has demonstrated the
superior performance of posterior exploration compared to
the state-of-the-art MCMC method in both synthetic examples
and real case studies and shows the potential for more
complex scenarios. The SVGD algorithm is proposed in an
attempt to tackle the multimodal posterior, which is a
challenge for many MCMC-type algorithms. Preliminary results
show that the posterior space in geological inversion with
gravity as the likelihood could be complex, and the
multimodal distribution is difficult to resolve in the
current configuration. This is intended to show the
possibility of applying SVGD to solve the model-based
inversion problem and indicates the need for further
improvement.},
cin = {532610 / 530000 / 080052},
ddc = {550},
cid = {$I:(DE-82)532610_20140620$ / $I:(DE-82)530000_20140620$ /
$I:(DE-82)080052_20160101$},
pnm = {GRK 2379 - GRK 2379: Hierarchische und hybride Ansätze
für moderne inverse Probleme (333849990)},
pid = {G:(GEPRIS)333849990},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2024-02206},
url = {https://publications.rwth-aachen.de/record/980351},
}
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