Fast Crystal Tensor Property Prediction: A General O(3)-Equivariant Framework Based on Polar Decomposition

Haowei Hua, Wanyu Lin, JINGWEN YANG

Keywords: $O(3)$ group tensor equivariance, polar decomposition, tensor properties

Abstract:

Predicting tensor properties of the crystalline materials is a fundamental task in materials science. Unlike single-value property prediction, which is inherently invariant, tensor property prediction requires maintaining $O(3)$ group tensor equivariance. This equivariance constraint often introduces tremendous computational costs, necessitating specialized designs for effective and efficient predictions.
To address this limitation, we propose a general $O(3)$-equivariant framework for fast crystal tensor prediction, called {\em GoeCTP}.
Our framework is efficient as it does not need to impose equivalence constraints onto the network architecture. Instead, {\em GoeCTP} captures the tensor equivariance with a simple external rotation and reflection (R\&R) module based on the polar decomposition. The crafted external R\&R module can rotate and reflect the crystal into an invariant standardized crystal position in space without introducing extra computational cost. We show that {\em GoeCTP} is general as it is a plug-and-play module that can be smoothly integrated with any existing single-value property prediction network for predicting tensor properties. Experimental results indicate that the {\em GoeCTP} method achieves higher prediction performance and runs 13$\times$ faster compared to existing state-of-the-art models in elastic benchmarking datasets, underscoring its effectiveness and efficiency.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 8483