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.
This paper is available in PDF form
.
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.
This paper is available in PDF form
.
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
.