Hybrid learning models for statistical continuum mechanics
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Kelly, Conlain
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Abstract
This document summarizes my research aimed at creating interpretable and useful machine
learning models to assist efforts in materials design. In particular, I focus on the problem of predict-
ing local response fields (stresses and strains) over heterogeneous structures subjected to boundary
loading conditions, also known as the localization problem. In a sense all of micromechanics con-
sists of elasticity plus defect motion; my doctoral work extensively explores the first half of that
equation in relation to machine learning. This thesis comprises three papers: an exploratory study
applying iterative neural networks to elastic localization, a thermodynamically-informed iterative
neural operator which generalizes these ideas to work over a wider range of microstructure classes
and loading directions, and an extrapolation study which explores how far neural operators can be
taken outside their training distribution by hybridizing them with FFT-based relaxation solvers. All
three papers focus on purely elastic deformations, but keep an eye on the long-term goal of mod-
eling time-dependent, dissipative deformations. These are contextualized as part of the general
stochastic inverse problem known as process-structure-property modeling.
Beyond the localization problem, I have been fortunate to collaborate on a number of works
which build up different parts of the process-structure-property linkage. Most of these efforts have
been published in the theses of Dr. Andreas Robertson and Dr. Adam Generale, so I only pro-
vide brief descriptions and summaries for each paper. In particular, I contextualize these works
as part of the increasing alignment between the fields of deep learning, numerical methods, and
continuum mechanics. The contributions of this thesis are thus twofold: to provide useful deep
learning models which allow exploration of the microstructure space, and to advance a shared lan-
guage bridging the conceptually-isolated fields of data-driven modeling and statistical continuum
mechanics.
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Date
2024-12-08
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Dissertation