mlsanityData to 14 Oct 2026

A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction

arXiv 2406.12888 ↗First posted 3 Jun 2024cond-mat.mtrl-sci cs.AI physics.atom-phcited by 8

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Abstract (arXiv)

We consider the prediction of general tensor properties of crystalline materials, including dielectric, piezoelectric, and elastic tensors. A key challenge here is how to make the predictions satisfy the unique tensor equivariance to O(3) group and invariance to crystal space groups. To this end, we propose a General Materials Tensor Network (GMTNet), which is carefully designed to satisfy the required symmetries. To evaluate our method, we curate a dataset and establish evaluation metrics that are tailored to the intricacies of crystal tensor predictions. Experimental results show that our GMTNet not only achieves promising performance on crystal tensors of various orders but also generates predictions fully consistent with the intrinsic crystal symmetries. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 22 of its 44 references that are in the map. First posted on arXiv 3 Jun 2024.

Builds on

22 of 44 references.

References · 22

  1. 2021E(n) Equivariant Graph Neural Networkscited by 965
  2. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  3. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 708
  4. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 571
  5. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 474
  6. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 441
  7. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 313
  8. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 270
  9. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 264
  10. 2022e3nn: Euclidean Neural Networkscited by 174
  11. 2021Spherical Message Passing for 3D Graph Networkscited by 168
  12. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 168
10 more
  1. 2018Universal approximations of invariant maps by neural networkscited by 127
  2. 2018Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputscited by 98
  3. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  4. 2023Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltoniancited by 39
  5. 2023Efficient Approximations of Complete Interatomic Potentials for Crystal Property Predictioncited by 37
  6. 2024Complete and Efficient Graph Transformers for Crystal Material Property Predictioncited by 34
  7. 2023A Latent Diffusion Model for Protein Structure Generationcited by 28
  8. 2023Towards Symmetry-Aware Generation of Periodic Materialscited by 26
  9. 2023Connectivity Optimized Nested Graph Networks for Crystal Structurescited by 11
  10. 2023M2Hub: Unlocking the Potential of Machine Learning for Materials Discoverycited by 8

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 4; 2026: 3.

8 papers.

  1. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 51
  2. 2025Space Group Equivariant Crystal Diffusioncited by 15
  3. 2025Toward Greater Autonomy in Materials Discovery Agents: Unifying Planning, Physics, and Scientistscited by 10
  4. 2025A Single Architecture for Representing Invariance Under Any Space Groupcited by 1
  5. 2026Efficient Equivariant High-Order Crystal Tensor Prediction via Cartesian Local-Environment Many-Body Couplingcited by 1
  6. 2026Exact Symmetry as Algebra: Group-Structured Tensors that Enforce Physical Selection Rulescited by 1
  7. 2024PDDFormer: Pairwise Distance Distribution Graph Transformer for Crystal Material Property Predictioncited by 0
  8. 2026The parity gap in crystal tensor predictioncited by 0