Equivariant Graph Neural Networks for Prediction of Tensor Material Properties of Crystals

TL;DR

This paper develops E(3)-equivariant graph neural networks to predict complex tensorial properties of crystals, leveraging symmetry-aware decompositions and demonstrating transferability across different property datasets.

Contribution

It introduces spherical harmonic decompositions for tensor properties and applies three E(3)-equivariant convolutional models for accurate, transferable predictions.

Findings

Models accurately predict dielectric, piezoelectric, and elasticity tensors.

Equivariant models outperform non-equivariant baselines.

Transferability of models across different tensor properties is demonstrated.

Abstract

Modern E(3)-Equivariant networks may be used to predict rotationally equivariant properties, including tensorial quantities. Three such quantities: the dielectric, piezoelectric, and elasticity tensors, are computationally expensive to produce ab initio for crystalline systems; however, with greater availability of such data in large material property databases, we now have a sufficient target space to begin training equivariant models in the prediction of such properties. Here we explicitly develop spherical harmonic decompositions of these tensorial properties using their general symmetries. We then apply three distinct E(3)-equivariant convolutional structures to the prediction of the components of these decompositions, allowing us to predict the aforementioned tensorial quantities in an equivariant manner and compare performance. We further report results testing the transferability of these predictive models between different tensorial target sets.