mlsanityData to 14 Oct 2026

Geometric and Physical Quantities Improve E(3) Equivariant Message Passing

arXiv 2110.02905 ↗First posted 6 Oct 2021cs.LG cs.AI stat.MLcited by 228

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Abstract (arXiv)

Including covariant information, such as position, force, velocity or spin is important in many tasks in computational physics and chemistry. We introduce Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that generalise equivariant graph networks, such that node and edge attributes are not restricted to invariant scalars, but can contain covariant information, such as vectors or tensors. This model, composed of steerable MLPs, is able to incorporate geometric and physical information in both the message and update functions. Through the definition of steerable node attributes, the MLPs provide a new class of activation functions for general use with steerable feature fields. We discuss ours and related work through the lens of equivariant non-linear convolutions, which further allows us to pin-point the successful components of SEGNNs: non-linear message aggregation improves upon classic linear (steerable) point convolutions; steerable messages improve upon recent equivariant graph networks that send invariant messages. We demonstrate the effectiveness of our method on several tasks in computational physics and chemistry and provide extensive ablation studies.

Key facts. Cited by 228 papers in the map (data through 14 Oct 2026). Builds on 46 of its 68 references that are in the map. First posted on arXiv 6 Oct 2021.

Builds on

46 of 68 references.

References · 46

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34 more
  1. 2014Deep Learning in Neural Networks: An Overviewcited by 770
  2. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
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  4. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 607
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  6. 2020Directional Message Passing for Molecular Graphscited by 561
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  8. 2019General E(2)-Equivariant Steerable CNNscited by 446
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 37; 2023: 52; 2024: 63; 2025: 47; 2026: 28.

228 papers.

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  1. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 474
  2. 2022Message Passing Neural PDE Solverscited by 386
  3. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 264
  4. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 256
  5. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 204
  6. 2022Graph neural networks for materials science and chemistrycited by 182
  7. 2022e3nn: Euclidean Neural Networkscited by 174
  8. 2023A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detectioncited by 145
  9. 2022EquiBind: Geometric Deep Learning for Drug Binding Structure Predictioncited by 144
  10. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  11. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 117
  12. 2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 101
38 more
  1. 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 98
  2. 2022Clifford Neural Layers for PDE Modelingcited by 92
  3. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 90
  4. 2022AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutionscited by 82
  5. 2023GTA: A Geometry-Aware Attention Mechanism for Multi-View Transformerscited by 79
  6. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 76
  7. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 73
  8. 2022Molecular Geometry Pretraining with SE(3)-Invariant Denoising Distance Matchingcited by 68
  9. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 68
  10. 2022MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Designcited by 66
  11. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 56
  12. 2023Clifford Group Equivariant Neural Networkscited by 55
  13. 2022Learning Symmetric Embeddings for Equivariant World Modelscited by 54
  14. 2023TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentialscited by 54
  15. 2024Does equivariance matter at scale?cited by 52
  16. 2023Geometric Algebra Transformercited by 48
  17. 2022Spherical Channels for Modeling Atomic Interactionscited by 47
  18. 2022Invariance Learning in Deep Neural Networks with Differentiable Laplace Approximationscited by 42
  19. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 41
  20. 2023Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltoniancited by 39
  21. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 36
  22. 2022State-specific protein-ligand complex structure prediction with a multi-scale deep generative modelcited by 35
  23. 2022ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networkscited by 31
  24. 2024Cartesian atomic cluster expansion for machine learning interatomic potentialscited by 31
  25. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  26. 2022SE(3)-Equivariant Attention Networks for Shape Reconstruction in Function Spacecited by 27
  27. 2023SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biasescited by 27
  28. 2023LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suitecited by 27
  29. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 27
  30. 2023QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Moleculescited by 26
  31. 2023Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Sciencecited by 25
  32. 2022Equivariant Graph Hierarchy-Based Neural Networkscited by 24
  33. 2023Coarse-to-Fine: a Hierarchical Diffusion Model for Molecule Generation in 3Dcited by 24
  34. 2023E(n) Equivariant Message Passing Simplicial Networkscited by 23
  35. 2024Improving Equivariant Model Training via Constraint Relaxationcited by 23
  36. 2025GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformercited by 23
  37. 2023Symmetry-Informed Geometric Representation for Molecules, Proteins, and Crystalline Materialscited by 22
  38. 2024Clifford Group Equivariant Simplicial Message Passing Networkscited by 22

50 most cited of 228 All 228 (JSON)