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

TL;DR

This work tackles the challenge of end-to-end high-order crystal tensor prediction, where traditional spherical-harmonic equivariant methods incur heavy compute costs at higher tensor orders. It introduces CEITNet, a Cartesian Environment Interaction Tensor Network that decouples invariant atomic encoding from equivariant tensor construction, constructs channelized local environments on Cartesian bases, and uses a learnable channel-interaction head to enable flexible many-body mixing. CEITNet achieves state-of-the-art accuracy on dielectric (order-2), piezoelectric (order-3), and elastic (order-4) tensor benchmarks while significantly reducing parameter count and runtime, demonstrating both predictive power and efficiency. The approach advances practical materials screening by enabling reliable high-order tensor predictions at scale and lays groundwork for extending Cartesian-based equivariant models to broader tensor tasks with improved symmetry alignment.

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.

Figures (1)

• Figure 1: The architecture of CEITNet. It integrates an invariant message passing backbone with a Cartesian-based local environment constructor. The tensor construction head employs a learnable interaction matrix $\mathbf{M}$ to capture flexible many-body interactions. Note that some engineering details are omitted in the diagram for clarity.