# StrainTensorNet: Predicting crystal structure elastic properties using SE(3)-equivariant graph neural networks

arXiv: https://arxiv.org/abs/2306.12818 · HTML: https://mlsanity.com/paper/2306.12818/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 55 references that are in the map.
- First posted on arXiv 22 Jun 2023.

## Builds on (most cited first, 13 of 13)

- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [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)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [On the Universality of Rotation Equivariant Point Cloud Networks](https://mlsanity.com/paper/2010.02449/) (2020)
- [Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties](https://mlsanity.com/paper/2008.08461/) (2020)
- [Predicting Elastic Properties of Materials from Electronic Charge Density Using 3D Deep Convolutional Neural Networks](https://mlsanity.com/paper/2003.13425/) (2020)

## Built on by (most cited first, 3 of 3)

- [CrystalGRW: Generative Modeling of Crystal Structures with Targeted Properties via Geodesic Random Walks](https://mlsanity.com/paper/2501.08998/) (2025)
- [FIRE-GNN: Force-informed, Relaxed Equivariance Graph Neural Network for Rapid and Accurate Prediction of Surface Properties](https://mlsanity.com/paper/2508.16012/) (2025)
- [High-Throughput Unsupervised Profiling of the Morphology of 316L Powder Particles for Use in Additive Manufacturing](https://mlsanity.com/paper/2512.06012/) (2025)

## Abstract (arXiv)

Accurately predicting the elastic properties of crystalline solids is vital for computational materials science. However, traditional atomistic scale ab initio approaches are computationally intensive, especially for studying complex materials with a large number of atoms in a unit cell. We introduce a novel data-driven approach to efficiently predict the elastic properties of crystal structures using SE(3)-equivariant graph neural networks (GNNs). This approach yields important scalar elastic moduli with the accuracy comparable to recent data-driven studies. Importantly, our symmetry-aware GNNs model also enables the prediction of the strain energy density (SED) and the associated elastic constants, the fundamental tensorial quantities that are significantly influenced by a material's crystallographic group. The model consistently distinguishes independent elements of SED tensors, in accordance with the symmetry of the crystal structures. Finally, our deep learning model possesses meaningful latent features, offering an interpretable prediction of the elastic properties.