mlsanityData to 7 Oct 2026

Equivariant Networks for Crystal Structures

arXiv 2211.15420 ↗First posted 15 Nov 2022cond-mat.mtrl-sci cs.LGcited by 24

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Abstract (arXiv)

Supervised learning with deep models has tremendous potential for applications in materials science. Recently, graph neural networks have been used in this context, drawing direct inspiration from models for molecules. However, materials are typically much more structured than molecules, which is a feature that these models do not leverage. In this work, we introduce a class of models that are equivariant with respect to crystalline symmetry groups. We do this by defining a generalization of the message passing operations that can be used with more general permutation groups, or that can alternatively be seen as defining an expressive convolution operation on the crystal graph. Empirically, these models achieve competitive results with state-of-the-art on property prediction tasks.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 39 of its 95 references that are in the map. First posted on arXiv 15 Nov 2022.

Builds on

39 of 95 references.

References · 39

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
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  8. 2016Group Equivariant Convolutional Networkscited by 1,154
  9. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  10. 2021E(n) Equivariant Graph Neural Networkscited by 951
  11. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  12. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
27 more
  1. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  2. 2020Directional Message Passing for Molecular Graphscited by 556
  3. 2018Spherical CNNscited by 452
  4. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  5. 2018Invariant and Equivariant Graph Networkscited by 339
  6. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  7. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  8. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 268
  9. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  10. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
  11. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  12. 2020Generalization and Representational Limits of Graph Neural Networkscited by 217
  13. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  14. 2021E(n) Equivariant Normalizing Flowscited by 165
  15. 2017Equivariance Through Parameter-Sharingcited by 139
  16. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  17. 2019Machine learning for molecular simulationcited by 109
  18. 2020On Learning Sets of Symmetric Elementscited by 97
  19. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  20. 2018Covariant Compositional Networks For Learning Graphscited by 54
  21. 2020Spin-Weighted Spherical CNNscited by 50
  22. 2020Finding Symmetry Breaking Order Parameters with Euclidean Neural Networkscited by 30
  23. 2019Reliable and Explainable Machine Learning Methods for Accelerated Material Discoverycited by 18
  24. 2021Multiset-Equivariant Set Prediction with Approximate Implicit Differentiationcited by 17
  25. 2021Equivariant Networks for Pixelized Spherescited by 16
  26. 2020Equivariant Maps for Hierarchical Structurescited by 11
  27. 2022A Simple and Universal Rotation Equivariant Point-cloud Networkcited by 11

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 7; 2024: 5; 2025: 6; 2026: 5.

24 papers.

Sort:

  1. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  2. 2025SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Modelscited by 48
  3. 2023LLM-Prop: Predicting Physical And Electronic Properties Of Crystalline Solids From Their Text Descriptionscited by 29
  4. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  5. 2023Symmetry Breaking and Equivariant Neural Networkscited by 24
  6. 2025Improving Equivariant Networks with Probabilistic Symmetry Breakingcited by 15
  7. 2023MatSciML: A Broad, Multi-Task Benchmark for Solid-State Materials Modelingcited by 14
  8. 2024AI-driven inverse design of materials: Past, present and futurecited by 10
  9. 2022Implicit Convolutional Kernels for Steerable CNNscited by 9
  10. 2023M2Hub: Unlocking the Potential of Machine Learning for Materials Discoverycited by 8
  11. 2024Improved Canonicalization for Model Agnostic Equivariancecited by 7
  12. 2024Supra-Laplacian Encoding for Transformer on Dynamic Graphscited by 6
12 more
  1. 2023Densely Connected G-invariant Deep Neural Networks with Signed Permutation Representationscited by 2
  2. 2026Equivariant Neural Networks for Force-Field Models of Lattice Systemscited by 2
  3. 2026Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theoriescited by 2
  4. 2023Equivariant Parameter Sharing for Porous Crystalline Materialscited by 1
  5. 2026Graph neural network force fields for adiabatic dynamics of lattice Hamiltonianscited by 1
  6. 2024Graph Neural Networks for Carbon Dioxide Adsorption Prediction in Aluminium-Exchanged Zeolitescited by 0
  7. 2025Symmetry-Informed Graph Neural Networks for Carbon Dioxide Isotherm and Adsorption Prediction in Aluminum-Substituted Zeolitescited by 0
  8. 2025Quotient Complex Transformer (QCformer) for Perovskite Data Analysiscited by 0
  9. 2025Fundamental Limits of Crystalline Equivariant Graph Neural Networks: A Circuit Complexity Perspectivecited by 0
  10. 2025High-Throughput Unsupervised Profiling of the Morphology of 316L Powder Particles for Use in Additive Manufacturingcited by 0
  11. 2026Magnetic HIP-NN for spin dynamics in disordered itinerant magnetscited by 0
  12. 2026Graph Neural Network Force Fields for Spin Dynamics in Metallic Magnetscited by 0