Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials

TL;DR

This paper introduces an energy-conserving, SE(3) equivariant graph neural network for predicting the elasticity of lattice-based metamaterials, demonstrating improved accuracy and efficiency over non-equivariant models.

Contribution

The work presents a novel higher-order GNN model with energy conservation and SE(3) equivariance, trained on a large dataset for lattice elasticity prediction, advancing physical principle-based modeling.

Findings

Model outperforms non-equivariant counterparts in accuracy

Reduces training data and computational requirements

Applicable to various fourth-order tensors beyond elasticity

Abstract

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.