MechE PhD Dissertation Defense: Lingxiao Yuan

TITLE: MACHINE LEARNING POWERED INSIGHTS INTO METAMATERIAL PREDICTION AND DESIGN

ABSTRACT: There has been significant recent interest in the mechanics community to apply machine learning methods to metamaterial prediction and design. Metamaterials are distinguished by their programmability, enabling the achievement of novel functionalities typically absent in conventional materials. Understanding metamaterials necessitates unraveling the intricate nonlinear relationship between design choices and mechanical properties. Machine learning (ML) stands out from traditional approaches by its capability to accurately approximate nonlinear relationships and rapidly predict properties across an extensive number of unexplored materials. While ML methods have enabled many breakthroughs,at least two critical questions remain unanswered. The first pertains to whether the assumptions underlying ML models remain validated when applied to real-world mechanics problems. The second question is whether ML models can facilitate the design of novel metamaterials with limited prior information. Our study is aimed at addressing these questions. In the first study, we examined the limitations of traditional machine learning (ML) models. These models assume that the training (observed) data and testing (unseen) data are independent and identically distributed (i.i.d). However, when applied to real-world mechanics problems with unknown test environments, these standard ML approaches can be very sensitive to data distribution shifts, and can break down when evaluated on test datasets that violate the i.i.d. assumption. In contrast, out-of-distribution (OOD) generalization approaches assume that the data contained in test environments are allowed to shift. To date, multiple methods have been proposed to improve the OOD generalization of ML methods. However, most of these OOD generalization methods have been focused on classification problems, driven in part by the lack of benchmark datasets available for OOD regression problems. Thus, the efficiency of these OOD generalization methods on regression problems, which are typically more relevant to mechanics research of metamaterials than classification problems, is unknown. To address this, we perform a fundamental study of OOD generalization methods for regression problems in mechanics. Specifically, we identify three OOD generalization problems: covariate shift, mechanism shift, and sampling bias. For each problem, we create two benchmark examples that extend the Mechanical MNIST dataset collection, and we investigate the performance of popular OOD generalization methods on these mechanics-specific regression problems. Our numerical experiments show that in most cases, while the OOD algorithms perform better compared to traditional ML methods on these OOD generalization problems, there is a compelling need to develop more robust OOD methods that can generalize the notion of invariance across multiple OOD scenarios. Overall, we expect that this study, as well as the associated open access benchmark datasets, will enable further development of OOD methods for mechanics specific regression problems. In the second study, we focus on the design of chiral metamaterials that can either violate reciprocity, or exhibit elastic asymmetry or odd elasticity. While these properties are highly desirable to enable mechanical metamaterials to exhibit novel wave propagation phenomena, it remains an open question as to how to design passive structures that exhibit both significant non-reciprocity and elastic asymmetry. In this study, we first define several design spaces for chiral metamaterials leveraging specific design parameters, including the ligament contact angles, the ligament shape, circle radius, and ligament length. Having defined the design spaces, we then leverage machine learning approaches, and specifically Bayesian optimization, to determine optimally performing designs within each design space satisfying maximal non-reciprocity or stiffness asymmetry. Finally, we perform multi-objective optimization by determining the Pareto optimum and find chiral metamaterials that simultaneously exhibit high non-reciprocity and stiffness asymmetry. Our analysis of the underlying mechanisms reveals that chiral metamaterials that can display multiple different contact states under loading in different directions are able to simultaneously exhibit both high non-reciprocity and stiffness asymmetry. Overall, this study demonstrates the effectiveness of employing ML to bring insights to a novel domain with limited prior information, and more generally will pave the way for metamaterials with unique properties and functionality in directing and guiding mechanical wave energy.

COMMITTEE: ADVISOR Professor Harold Park, ME/MSE; CHAIR Professor Kamil Ekinci, ME/MSE; Professor Emma Lejeune, ME; Professor Douglas Holmes, ME/MSE; Professor Paul Barbone, ME/MSE