Towards Out of Distribution Generalization for Problems in Mechanics

L. Yuan, H.S. Park and E. Lejeune
Computer Methods in Applied Mechanics and Engineering 2022; 400:115569

Abstract

There has been a massive increase in research interest towards applying data driven methods to problems in mechanics, with a particular emphasis on using data driven methods for predictive modeling and design of materials with novel functionality. While traditional machine learning (ML) methods have enabled many breakthroughs, they rely on the assumption that the training (observed) data and testing (unseen) data are independent and identically distributed (i.i.d). However, when these standard ML approaches are applied to real world mechanics problems with unknown test environments, they 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 (i.e., violate the i.i.d. assumption). 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 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.

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Forward and Inverse Design of Kirigami via Supervised Autoencoder

P.Z. Hanakata, E.D. Cubuk, D.K. Campbell and H.S. Park
Physical Review Research (Rapid Communications) 2020; 2:042006(R)

Abstract

Machine learning (ML) methods have recently been used as forward solvers to predict the mechanical properties of composite materials. Here, we use a supervised-autoencoder (sAE) to perform inverse design of graphene kirigami, where predicting the ultimate stress or strain under tensile loading is known to be difficult due to nonlinear effects arising from the out-of-plane buckling. Unlike the standard autoencoder, our sAE is able not only to reconstruct cut configurations but also to predict mechanical properties of graphene kirigami and classify the kirigami with either parallel or orthogonal cuts. By interpolating in the latent space of kirigami structures, the sAE is able to generate novel designs that mix parallel and orthogonal cuts, despite being trained independently on parallel or orthogonal cuts. Our method allows us to both identify novel designs and predict, with reasonable accuracy, their mechanical properties, which is crucial for expanding the search space for materials design.

This paper is available in PDF form .


Machine Learning-Based Design of Porous Graphene with Low Thermal Conductivity

J. Wan, J-W Jiang and H.S. Park
Carbon 2020; 157:262-269

Abstract

The thermal conductivity of two-dimensional materials like graphene can efficiently be tuned by introducing holes, in which the density and distribution of the holes are the key parameters. Furthermore, the distribution of holes can induce a variation as high as 74% in the thermal conductivity for porous graphene with a given density of holes. Therefore, an existing challenge is to find the optimal distribution of holes that can minimize or maximize the thermal conductivity of porous graphene as the design space expands dramatically with increasing hole density. We therefore apply an inverse design methodology based on machine learning to reveal the relationship between hole distribution and thermal conductivity reduction in monolayer graphene. The methodology reveals that holes that are randomly distributed transverse to the direction of heat flow, but that exhibit some periodicity along the direction of heat flow, represent the optimal distribution to minimizing the thermal conductivity for porous graphene. Lattice dynamics calculations and wave packet simulations reveal that this spatial distribution effectively causes localization of the phonon modes in porous graphene, which reduces the thermal conductivity. Overall, this work demonstrates the power of machine learning-based design approaches to efficiently obtain new physical insights for scientific problems of interest.

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Accelerated Search and Design of Stretchable Graphene Kirigami Using Machine Learning

P.Z. Hanakata, E.D. Cubuk, D.K. Campbell and H.S. Park
Physical Review Letters 2018; 121:255304

Abstract

Making kirigami-inspired cuts into a sheet has been shown to be an effective way of designing stretchable materials with metamorphic properties where the 2D shape can transform into complex 3D shapes. However, finding the optimal solutions is not straightforward as the number of possible cutting patterns grows exponentially with system size. Here, we report on how machine learning (ML) can be used to approximate the target properties, such as yield stress and yield strain, as a function of cutting pattern. Our approach enables the rapid discovery of kirigami designs that yield extreme stretchability as verified by molecular dynamics (MD) simulations. We find that convolutional neural networks (CNN), commonly used for classification in vision tasks, can be applied for regression to achieve an accuracy close to the precision of the MD simulations. This approach can then be used to search for optimal designs that maximize elastic stretchability with only 1000 training samples in a large design space of ~4x106 candidate designs. This example demonstrates the power and potential of ML in finding optimal kirigami designs at a fraction of iterations that would be required of a purely MD or experiment-based approach, where no prior knowledge of the governing physics is known or available.

This paper is available in PDF form .