Predicting elastic properties of crystal structures using rotationally equivariant graph neural networks

The advent of machine learning (ML) enables data-driven approaches for computational materials science. With sufficient data from first principles, e.g. density functional theory, well-developed ML models can predict properties of unseen materials with high accuracy. Despite its empirical success, standard black box ML models lack explainability, and often are uninformed of material physics. In this work, we apply the recently developed ML model that is aware of symmetry groups possessed by crystal structures, to predict the elastic property of crystalline solids. Specifically, we train graph neural networks designed to learn rotational equivariance of three-dimensional objects to predict the strain energy tensors computed from the elastic tensors of crystalline solids. Although the strain energy tensor has 6 x 6 components, the number of independent components crucially depend on the symmetries of the crystals. Our physics-informed ML model can predict the strain energy tensor of unseen crystal structures rather accurately, and symmetry-induced tensor components are considerably differentiated. Our work is a stepping stone towards the data-driven discovery of materials with desirable properties.