Machine Learning and Inference Methods for Surrogate Modeling and Inexpensive Characterization of Elastodynamic Systems

Citation

Ogren, Alexander Charles (2024) Machine Learning and Inference Methods for Surrogate Modeling and Inexpensive Characterization of Elastodynamic Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/dcbz-sj62. https://resolver.caltech.edu/CaltechTHESIS:06042024-004152477

Abstract

This thesis has two main focuses: (1) surrogate modeling of elastodynamic systems, and (2) inference methods for the inexpensive characterization of elastodynamic systems. Elastodynamics is the study of how and why materials move and deform when they are subject to time-varying loads, covering a wide range of applications from architected materials, to telecommunications, seismology, sound isolation, non-destructive evaluation, and medical imaging. Here, we explore how to more efficiently model elastodynamics, and what we can infer about our environment from observing them.

The next generation of material engineering aims to leverage advanced multi-functional control over elastodynamic behaviors, but is currently limited by the large computational cost of purely physics-based modeling methods. Surrogate models aim to alleviate this cost by providing a data-driven approach to evaluate engineered material systems more efficiently. However, most current surrogate models lack certain useful traits, diminishing their potential for real-world use. This thesis begins by surveying the current state of surrogate modeling techniques, and establishes a set of state-of-the-art traits that greatly augment the utility of surrogate models, offering a perspective for the future direction of the field.

Next, a data-driven surrogate model based on Gaussian process regression for the computation of dispersion relations is developed, GPR-dispersion. The model exhibits several of the aforementioned traits, including representation invariance, data efficiency, incorporating direct use of physical theories, and the provision of both uncertainty estimates on its predictions and gradients for compatibility with gradient-based design optimization methods. GPR-dispersion is evaluated in comparison against both deep learning and traditional physics-based models.

The thesis then pivots to inference methods for the inexpensive characterization of material systems via partial observation of elastodynamic behaviors. Tissue stiffness is a tremendously important biomarker for a long list of health conditions, but often needs to be evaluated in a medical clinic with expensive equipment and highly trained workers. At-home health monitoring is a major next-generation goal of healthcare, but the trajectories of current consumer-grade sensor technology and biomarker inference methods have not yet fully intersected.

Inspired by a related work (Visual Vibration Tomography), Visual Surface Wave Tomography (VSWT) is proposed. VSWT observes partial information about the surface waves of layered elastodynamic systems (such as biological tissue) through monocular video to infer subsurface constitutive and geometrical information. Simulated experiments are presented to evaluate the accuracy, sensitivity, and limits of the method under ideal conditions. Real-world experimental results are presented using phantom materials that emulate biological tissue to demonstrate a practical proof of concept.

Thesis Files