Data-Driven and Physics-Constrained Deep Learning for Surrogate Modeling and Uncertainty Quantification of Physical Systems

Doctoral Dissertation

Abstract

Surrogate modeling is computationally attractive for problems that require repetitive yet expensive simulations of PDEs, such as uncertainty propagation, deterministic design or inverse problems, where the main challenges are curse of dimensionality, data efficiency, uncertainty quantification and generalization, especially for problems with high dimensional input. To tackle those issues, we propose an image-to-image regression approach with deep dense convolutional encoder-decoder networks to learn accurate surrogate models for problems with up to 4225 input dimensions that is out of the reach of traditional surrogate models. A Stein variational inference method is scaled to modern Bayesian deep neural networks to further boost the regression performance and provide well-calibrated uncertainty estimate even with limited training data. We further explore how to incorporate the governing equations of the physical models into the loss/likelihood functions of the physics-constrained surrogates to completely avoid any simulation (or labeled data) while achieving similar accuracy with the date-driven surrogates. A conditional flow-based generative model with reverse KL-divergence loss without labeled data is trained to capture the predictive uncertainty. We also extend those methods to dynamic problems by treating time as extra input for dynamic multiphase flow. The efficacy of those methods are demonstrated in a variety of surrogate modeling and uncertainty quantification tasks in heterogeneous porous media flow.

Attributes

Attribute NameValues
Author Yinhao Zhu
Contributor Panos Antsaklis, Committee Member
Contributor Lizhen Lin, Committee Member
Contributor Nicholas Zabaras, Research Director
Contributor Walter Scheirer, Committee Member
Degree Level Doctoral Dissertation
Degree Discipline Electrical Engineering
Degree Name Doctor of Philosophy
Banner Code
  • PHD-EE

Defense Date
  • 2019-08-23

Submission Date 2019-11-17
Subject
  • surrogate modeling, uncertainty quantification, image translation, Bayesian neural networks, Stein variational gradient descent, normalizing flow, generative models, physics-constrained, energy-based models, porous media flow

Record Visibility Public
Content License
  • All rights reserved

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