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

2024-10-03

arXiv.org

AI Summary

Predicting tensorial properties of crystalline materials requires O(3)-equivariance, yet conventional approaches rely on custom-designed equivariant architectures, incurring substantial computational overhead. This work proposes a general, efficient framework that achieves equivariance without architectural modifications. We introduce the first extrinsic Rotation-and-Reflection (R&R) module based on polar decomposition, which geometrically normalizes input crystal structures into a rotation-and-reflection invariant space—enabling equivariant modeling with zero additional parameters or computational cost. The module is plug-and-play and fully compatible with any scalar-property prediction model. Evaluated on the elastic tensor benchmark, our method surpasses existing state-of-the-art models in accuracy while accelerating inference by 13×, thereby achieving an unprecedented balance among equivariance, generality, and efficiency.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Other Foundations of Computer Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Predicting the tensor properties of 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 property prediction, called GoeCTP. Our framework is efficient as it does not need to impose equivalence constraints onto the network architecture. Instead, GoeCTP captures the tensor equivariance with a simple external rotation and reflection (R&R) module based on 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 GoeCTP is general as it is a plug-and-play module that can be smoothly integrated with any existing single-value property prediction framework for predicting tensor properties. Experimental results indicate that GoeCTP achieves higher prediction performance and runs 13$ imes$ faster compared to existing state-of-the-art methods in elastic benchmarking datasets, underscoring its effectiveness and efficiency.

Problem

• Predicting tensor properties of crystals with O(3) equivariance
• Reducing computational costs in tensor property prediction
• Ensuring fast and accurate crystal property prediction

Innovation

• Uses polar decomposition for canonicalization
• Ensures O(3)-equivariant tensor prediction
• Achieves fast and accurate results