Energy-conserving equivariant GNN for elasticity of lattice architected metamaterials
This work provides a faster surrogate model for material scientists and engineers designing metamaterials, though it is incremental as it builds on existing GNN methods with added physical constraints.
The authors tackled the problem of predicting elasticity in lattice architected metamaterials by developing an SE(3)-equivariant graph neural network that conserves energy, achieving improved predictive performance and reduced training requirements compared to non-equivariant models.
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.