A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction

TL;DR

This paper introduces GMTNet, a neural network designed to predict tensor properties of crystalline materials while respecting their inherent symmetries, achieving accurate and symmetry-consistent results.

Contribution

The paper presents a novel symmetry-informed neural network architecture, GMTNet, tailored for crystal tensor prediction that ensures equivariance and invariance to relevant symmetry groups.

Findings

Achieves promising performance on various crystal tensor predictions

Generates symmetry-consistent tensor predictions

Provides a curated dataset and evaluation metrics for crystal tensors

Abstract

We consider the prediction of general tensor properties of crystalline materials, including dielectric, piezoelectric, and elastic tensors. A key challenge here is how to make the predictions satisfy the unique tensor equivariance to O(3) group and invariance to crystal space groups. To this end, we propose a General Materials Tensor Network (GMTNet), which is carefully designed to satisfy the required symmetries. To evaluate our method, we curate a dataset and establish evaluation metrics that are tailored to the intricacies of crystal tensor predictions. Experimental results show that our GMTNet not only achieves promising performance on crystal tensors of various orders but also generates predictions fully consistent with the intrinsic crystal symmetries. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).