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

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 learnable channel-space interactions. 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.

Materials have directional physical properties, such as dielectric, piezoelectric, and elastic responses. Predicting these properties from crystal structures is important for materials discovery, but physics-based simulations are often expensive. We introduce CEITNet, a machine learning model that represents crystals using simple 3D geometric building blocks. Through its design, CEITNet efficiently captures many-body interactions, learning how groups of neighboring atoms jointly influence a material’s response. The model also keeps predictions physically consistent when the crystal is rotated. On dielectric, piezoelectric, and elastic property prediction tasks, CEITNet achieves strong accuracy while remaining efficient. This makes it useful for large-scale screening of crystals with desirable directional properties.