(95d) Machine Learning Full Elastic Tensors of Inorganic Materials with Equivariant Neural Networks

The elastic tensor of an inorganic compound provides a complete description of the response of the material to external load in the elastic limit, from which any scalar elastic properties such as Young’s modulus and Poisson’s ratio can be obtained. The elastic tensor has two unique characteristics regarding symmetry. First, it transforms equivariantly w.r.t. to the operation of the Cartesian coordinates (specifically rotation), and second, it respects the space group of the material. This presents a significant challenge for building machine learning models to predict the elastic tensors. In this talk, we discuss our equivariant graph neural networks that automatically satisfy both requirements. Unlike many other machine learning models for predicting scalar elastic properties, where one model should be built for each property, our model universally predicts the full elastic tensor, and then other elastic properties can be obtained directly from it. We will show numerical results to demonstrate the effectiveness of the equivariant graph neural network model. It can also be applied to other tensorial properties such as NMR chemical shift tensors and piezoelectric tensors of inorganic materials.