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

arXiv 2602.04323 ↗First posted 4 Feb 2026cs.LG cs.AIcited by 0

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Abstract (arXiv)

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.

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References · 23

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  3. 2021E(n) Equivariant Graph Neural Networkscited by 951
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  5. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  6. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  7. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
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  10. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  11. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  12. 2022Equivariance with Learned Canonicalization Functionscited by 106
11 more
  1. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  2. 2023TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentialscited by 53
  3. 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 41
  4. 2024Complete and Efficient Graph Transformers for Crystal Material Property Predictioncited by 34
  5. 2024Cartesian atomic cluster expansion for machine learning interatomic potentialscited by 31
  6. 2024Crystalline Material Discovery in the Era of Artificial Intelligencecited by 11
  7. 2024A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Predictioncited by 7
  8. 2024Universal Machine Learning Kohn-Sham Hamiltonian for Materialscited by 3
  9. 2024Revisiting the Canonicalization for Fast and Accurate Crystal Tensor Property Predictioncited by 2
  10. 2022Edge-based Tensor prediction via graph neural networkscited by 1
  11. 2025Local-Global Associative Frames for Symmetry-Preserving Crystal Structure Modelingcited by 1

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