Mechanical MNIST: A benchmark dataset for mechanical metamodels

Lejeune, Emma

doi:10.1016/j.eml.2020.100659

Cited by 46 publications

(23 citation statements)

References 44 publications

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“…For this example, our goal is to learn the operator that maps initial deformations to later-time deformations in the equi-biaxial extension benchmark from the Mechanical MNIST database [67]. The data set is constructed from the results of 70, 000 finite-element simulations of a heterogeneous material subject to large deformations.…”

Section: F53 Mechanical Mnistmentioning

confidence: 99%

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Learning Operators with Coupled Attention

Kissas¹,

Seidman²,

Guilhoto³

et al. 2022

Preprint

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Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a novel operator learning method, LOCA (Learning Operators with Coupled Attention), motivated from the recent success of the attention mechanism. In our architecture, the input functions are mapped to a finite set of features which are then averaged with attention weights that depend on the output query locations. By coupling these attention weights together with an integral transform, LOCA is able to explicitly learn correlations in the target output functions, enabling us to approximate nonlinear operators even when the number of output function in the training set measurements is very small. Our formulation is accompanied by rigorous approximation theoretic guarantees on the universal expressiveness of the proposed model. Empirically, we evaluate the performance of LOCA on several operator learning scenarios involving systems governed by ordinary and partial differential equations, as well as a black-box climate prediction problem. Through these scenarios we demonstrate state of the art accuracy, robustness with respect to noisy input data, and a consistently small spread of errors over testing data sets, even for out-of-distribution prediction tasks.

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Section: F53 Mechanical Mnistmentioning

confidence: 99%

“…The data set is constructed from the results of 70, 000 finite-element simulations of a heterogeneous material subject to large deformations. MNIST images are considered to define a heterogeneous block of material described by a compressible Neo-Hookean model [67].…”

Section: F53 Mechanical Mnistmentioning

confidence: 99%

Learning Operators with Coupled Attention

Kissas¹,

Seidman²,

Guilhoto³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…While the mechanical property predictions of the sAE for structures that are significantly different (far from the training data) are less accurate, the sAE can still be utilized to propose novel designs. As online databases for mechanical systems, such as the mechanical MNIST database [32], are developed, our model will be important for learning the underlying physics in a reduced-dimensional space, as well as for proposing novel designs. Moreover, as the local structures are tightly connected to electronic properties, this method can be extended for learning electronic properties in 2D materials, such as pseudomagnetic and electric polarization, as a function of defects or kirigami cut patterns [33][34][35][36][37][38].…”

Section: Discussionmentioning

confidence: 99%

Forward and Inverse Design of Kirigami via Supervised Autoencoder

Hanakata,

Cubuk,

Campbell

et al. 2020

Preprint

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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.

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“…The FEniCS Project has been used within a wide range of research fields, such as tidal energy, geoscience, fluid mechanics, theoretical biology, strain gradient elasticity, biophysics and metamodelling ( Abali, 2019 ; Epanchintsev et al., 2016 ; Funke et al., 2019 ; Goodwin et al., 2019 ; Haagenson et al., 2020 ; Janečka et al., 2019 ; Lejeune, 2020 ; Murray and Young, 2020 ; Phunpeng and Baiz, 2015 ; Zhu and Yan, 2019 ). Abali (2017) , for instance, demonstrated several modelling examples with different engineering applications through a continuum mechanics approach.…”

Section: Introductionmentioning

confidence: 99%

Proposal of an open-source computational toolbox for solving PDEs in the context of chemical reaction engineering using FEniCS and complementary components

Ortiz-Laverde

Rengifo

Cobo

et al. 2021

Heliyon

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In this contribution, an open-source computational toolbox composed of FEniCS and complementary packages is introduced to the chemical and process engineering field by addressing two case studies. First, the oxidation of oxylene to phthalic anhydride is modelled and used as a FEniCS 0 proof-of-concept based on a comparison with the software Aspen Custom Modeler (ACM). The results show a maximum absolute error of 2% and thus a good FEniCS/ACM agreement. Second, synthetic natural gas (SNG) production through CO 2 methanation is covered in further detail. In this instance, a parametric study is performed for a tube bundle fixed-bed reactor employing a two-dimensional and transient pseudo-homogeneous model. An operating window for critical variables is evaluated, discussed, and successfully contrasted with the literature. Therefore, the computational toolbox methodology and the consistency of the results are validated, strengthening FEniCS and complements as an interesting alternative to solve mathematical models concerning chemical reaction engineering.

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Mechanical MNIST: A benchmark dataset for mechanical metamodels

Cited by 46 publications

References 44 publications

Learning Operators with Coupled Attention

Learning Operators with Coupled Attention

Forward and Inverse Design of Kirigami via Supervised Autoencoder

Proposal of an open-source computational toolbox for solving PDEs in the context of chemical reaction engineering using FEniCS and complementary components

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