Energy-conserving Equivariant GNN for Elasticity of Lattice Architected Metamaterials

Lattices are architected metamaterials whose properties strongly depend ontheir geometrical design. The analogy between lattices and graphs enables theuse of graph neural networks (GNNs) as a faster surrogate model compared totraditional methods such as finite element modelling. In this work we present ahigher-order GNN model trained to predict the fourth-order stiffness tensor ofperiodic strut-based lattices. The key features of the model are (i) SE(3)equivariance, and (ii) consistency with the thermodynamic law of conservationof energy. We compare the model to non-equivariant models based on a number oferror metrics and demonstrate the benefits of the encoded equivariance andenergy conservation in terms of predictive performance and reduced trainingrequirements.