Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials

Fuente: arXiv
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Main Authors: Grega, Ivan, Batatia, Ilyes, Csányi, Gábor, Karlapati, Sri, Deshpande, Vikram S.
Format: Preprint
Published: 2024
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author Grega, Ivan
Batatia, Ilyes
Csányi, Gábor
Karlapati, Sri
Deshpande, Vikram S.
author_facet Grega, Ivan
Batatia, Ilyes
Csányi, Gábor
Karlapati, Sri
Deshpande, Vikram S.
contents Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.
format Preprint
id arxiv_https___arxiv_org_abs_2401_16914
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials
Grega, Ivan
Batatia, Ilyes
Csányi, Gábor
Karlapati, Sri
Deshpande, Vikram S.
Machine Learning
Materials Science
Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.
title Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials
topic Machine Learning
Materials Science
url https://arxiv.org/abs/2401.16914