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

TL;DR

This paper introduces CEITNet, a Cartesian-based tensor network that efficiently predicts high-order crystal tensor properties, outperforming previous methods in accuracy and computational cost.

Contribution

The paper presents CEITNet, a novel Cartesian local environment tensor network that enables efficient high-order tensor prediction in crystal structures.

Findings

CEITNet surpasses prior methods in accuracy for high-order tensor prediction.

CEITNet offers high computational efficiency for complex tensor predictions.

CEITNet effectively predicts dielectric, piezoelectric, and elastic tensors across benchmarks.

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.