Efficient Equivariant High-Order Crystal Tensor Prediction via Cartesian Local-Environment Many-Body Coupling

2026-02-04

AI Summary

This work addresses the significant computational and memory challenges in end-to-end prediction of high-order crystal tensor properties—such as dielectric, piezoelectric, and elastic tensors—particularly when employing spherical harmonic equivariant models for high-rank targets. To overcome these limitations, the authors propose CEITNet, a novel architecture that constructs multi-channel Cartesian local environment tensors and introduces learnable many-body interactions directly in channel space, thereby eliminating the need for traditional Clebsch–Gordan coupling in spherical harmonic bases. This approach rigorously preserves equivariance while substantially enhancing both model expressiveness and computational efficiency. Experimental results demonstrate that CEITNet consistently outperforms existing methods across second- to fourth-order tensor prediction tasks, achieving higher accuracy with reduced computational cost.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Other Foundations of Computer Vision
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

End-to-end prediction of high-order crystal tensor properties from atomic structures remains challenging: while spherical-harmonic equivariant models are expressive, their Clebsch-Gordan tensor products incur substantial compute and memory costs for higher-order targets. We propose the Cartesian Environment Interaction Tensor Network (CEITNet), an approach that constructs a multi-channel Cartesian local environment tensor for each atom and performs flexible many-body mixing via a learnable channel-space interaction. By performing learning in channel space and using Cartesian tensor bases to assemble equivariant outputs, CEITNet enables efficient construction of high-order tensor. Across benchmark datasets for order-2 dielectric, order-3 piezoelectric, and order-4 elastic tensor prediction, CEITNet surpasses prior high-order prediction methods on key accuracy criteria while offering high computational efficiency.

Problem

• equivariant
• high-order tensor
• crystal property prediction
• computational efficiency
• many-body interaction

Innovation

• equivariant learning
• Cartesian tensor
• many-body interaction
• high-order tensor prediction
• CEITNet