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

arXiv: https://arxiv.org/abs/2406.12888 · HTML: https://mlsanity.com/paper/2406.12888/

## 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 (most cited first, 22 of 22)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Universal approximations of invariant maps by neural networks](https://mlsanity.com/paper/1804.10306/) (2018)
- [Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs](https://mlsanity.com/paper/1811.01900/) (2018)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian](https://mlsanity.com/paper/2306.04922/) (2023)
- [Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction](https://mlsanity.com/paper/2306.10045/) (2023)
- [Complete and Efficient Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2403.11857/) (2024)
- [A Latent Diffusion Model for Protein Structure Generation](https://mlsanity.com/paper/2305.04120/) (2023)
- [Towards Symmetry-Aware Generation of Periodic Materials](https://mlsanity.com/paper/2307.02707/) (2023)
- [Connectivity Optimized Nested Graph Networks for Crystal Structures](https://mlsanity.com/paper/2302.14102/) (2023)
- [M2Hub: Unlocking the Potential of Machine Learning for Materials Discovery](https://mlsanity.com/paper/2307.05378/) (2023)

## Built on by (most cited first, 8 of 8)

- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Space Group Equivariant Crystal Diffusion](https://mlsanity.com/paper/2505.10994/) (2025)
- [Toward Greater Autonomy in Materials Discovery Agents: Unifying Planning, Physics, and Scientists](https://mlsanity.com/paper/2506.05616/) (2025)
- [A Single Architecture for Representing Invariance Under Any Space Group](https://mlsanity.com/paper/2512.13989/) (2025)
- [Efficient Equivariant High-Order Crystal Tensor Prediction via Cartesian Local-Environment Many-Body Coupling](https://mlsanity.com/paper/2602.04323/) (2026)
- [Exact Symmetry as Algebra: Group-Structured Tensors that Enforce Physical Selection Rules](https://mlsanity.com/paper/2605.20440/) (2026)
- [PDDFormer: Pairwise Distance Distribution Graph Transformer for Crystal Material Property Prediction](https://mlsanity.com/paper/2408.12984/) (2024)
- [The parity gap in crystal tensor prediction](https://mlsanity.com/paper/2608.18714/) (2026)

## 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).