mlsanityData to 7 Oct 2026

FAENet: Frame Averaging Equivariant GNN for Materials Modeling

arXiv 2305.05577 ↗First posted 28 Apr 2023cs.LGcited by 72

Not on the map. Why?

Abstract (arXiv)

Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they enforce symmetries via the model architecture, which often reduces their expressivity, scalability and comprehensibility. In this paper, we introduce (1) a flexible framework relying on stochastic frame-averaging (SFA) to make any model E(3)-equivariant or invariant through data transformations. (2) FAENet: a simple, fast and expressive GNN, optimized for SFA, that processes geometric information without any symmetrypreserving design constraints. We prove the validity of our method theoretically and empirically demonstrate its superior accuracy and computational scalability in materials modeling on the OC20 dataset (S2EF, IS2RE) as well as common molecular modeling tasks (QM9, QM7-X). A package implementation is available at https://faenet.readthedocs.io.

Key facts. Cited by 72 papers in the map (data through 7 Oct 2026). Builds on 39 of its 61 references that are in the map. First posted on arXiv 28 Apr 2023.

Builds on

39 of 61 references.

References · 39

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2018How Powerful are Graph Neural Networks?cited by 4,355
  3. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  4. 2021E(n) Equivariant Graph Neural Networkscited by 951
  5. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  6. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  7. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  8. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  9. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  10. 2020Directional Message Passing for Molecular Graphscited by 556
  11. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  12. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
27 more
  1. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  2. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  3. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  4. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  5. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
  6. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  7. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
  8. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  9. 2018Universal approximations of invariant maps by neural networkscited by 127
  10. 2020GraphNorm: A Principled Approach to Accelerating Graph Neural Network Trainingcited by 116
  11. 2021Geometric Deep Learning on Molecular Representationscited by 113
  12. 2021SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effectscited by 103
  13. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  14. 2021Equivariant Point Network for 3D Point Cloud Analysiscited by 81
  15. 2022ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphscited by 69
  16. 2022GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasetscited by 61
  17. 2021ForceNet: A Graph Neural Network for Large-Scale Quantum Calculationscited by 58
  18. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  19. 2021Rotation Invariant Graph Neural Networks using Spin Convolutionscited by 52
  20. 2020An Introduction to Electrocatalyst Design using Machine Learning for Renewable Energy Storagecited by 45
  21. 2021Simple GNN Regularisation for 3D Molecular Property Prediction & Beyondcited by 44
  22. 2022So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systemscited by 39
  23. 2021Learning 3D Representations of Molecular Chirality with Invariance to Bond Rotationscited by 29
  24. 2022Equivariance versus Augmentation for Spherical Imagescited by 24
  25. 2022Graph Neural Network with Local Frame for Molecular Potential Energy Surfacecited by 14
  26. 2022The Open MatSci ML Toolkit: A Flexible Framework for Machine Learning in Materials Sciencecited by 14
  27. 2022PhAST: Physics-Aware, Scalable, and Task-specific GNNs for Accelerated Catalyst Designcited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 9; 2024: 25; 2025: 27; 2026: 11.

72 papers.

Sort:

By area:

  1. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  2. 2024Equivariant Frames and the Impossibility of Continuous Canonicalizationcited by 41
  3. 2023Smooth, exact rotational symmetrization for deep learning on point cloudscited by 39
  4. 2023Crystal-GFN: sampling crystals with desirable properties and constraintscited by 29
  5. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  6. 2024A Canonicalization Perspective on Invariant and Equivariant Learningcited by 25
  7. 2024Application-Driven Innovation in Machine Learningcited by 24
  8. 2024Generalizing Denoising to Non-Equilibrium Structures Improves Equivariant Force Fieldscited by 18
  9. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 18
  10. 2024Are High-Degree Representations Really Unnecessary in Equivariant Graph Neural Networks?cited by 18
  11. 2024Crystalformer: Infinitely Connected Attention for Periodic Structure Encodingcited by 15
  12. 2025Space Group Equivariant Crystal Diffusioncited by 15
38 more
  1. 2023MatSciML: A Broad, Multi-Task Benchmark for Solid-State Materials Modelingcited by 14
  2. 2024Probing the effects of broken symmetries in machine learningcited by 13
  3. 2024Relaxed Equivariance via Multitask Learningcited by 13
  4. 2024Gegenbauer Graph Neural Networks for Time-varying Signal Reconstructioncited by 12
  5. 2023Efficient Equivariant Transfer Learning from Pretrained Modelscited by 11
  6. 2024On the Completeness of Invariant Geometric Deep Learning Modelscited by 11
  7. 2024Predicting solvation free energies with an implicit solvent machine learning potentialcited by 10
  8. 2025ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitalscited by 9
  9. 2024Beyond Sequence: Impact of Geometric Context for RNA Property Predictioncited by 8
  10. 2024Improved Canonicalization for Model Agnostic Equivariancecited by 7
  11. 2024Object-Centric Temporal Consistency via Conditional Autoregressive Inductive Biasescited by 5
  12. 2024Stiefel Flow Matching for Moment-Constrained Structure Elucidationcited by 5
  13. 2025Learning Inter-Atomic Potentials without Explicit Equivariancecited by 5
  14. 2025Stress-Testing Multimodal Foundation Models for Crystallographic Reasoningcited by 4
  15. 2025Dynamic Triangulation-Based Graph Rewiring for Graph Neural Networkscited by 4
  16. 2025LeMat-Traj: A Scalable and Unified Dataset of Materials Trajectories for Atomistic Modelingcited by 4
  17. 2025Scaling Laws and Symmetry, Evidence from Neural Force Fieldscited by 4
  18. 2024Structure Preserving Diffusion Modelscited by 3
  19. 2024On the design space between molecular mechanics and machine learning force fieldscited by 3
  20. 2025ADMP-GNN: Adaptive Depth Message Passing GNNcited by 3
  21. 2025Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent Spacecited by 3
  22. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  23. 2025Catalyst GFlowNet for electrocatalyst design: A hydrogen evolution reaction case studycited by 3
  24. 2025Universally Invariant Learning in Equivariant GNNscited by 3
  25. 2023Reflection-Equivariant Diffusion for 3D Structure Determination from Isotopologue Rotational Spectra in Natural Abundancecited by 2
  26. 2023Predicting and Interpreting Energy Barriers of Metallic Glasses with Graph Neural Networkscited by 2
  27. 2024Graph Neural Network Generalization with Gaussian Mixture Model Based Augmentationcited by 2
  28. 2025AlphaNet: Scaling Up Local-frame-based Atomistic Interatomic Potentialcited by 2
  29. 2025Enhancing Machine Learning Potentials through Transfer Learning across Chemical Elementscited by 2
  30. 2025Continuous Simplicial Neural Networkscited by 2
  31. 2025CP2: Leveraging Geometry for Conformal Prediction via Canonicalizationcited by 2
  32. 2025Generalized Spherical Neural Operators: Green's Function Formulationcited by 2
  33. 2026SLayerGen: a Crystal Generative Model for all Space and Layer Groupscited by 2
  34. 2023On the importance of catalyst-adsorbate 3D interactions for relaxed energy predictionscited by 1
  35. 2023Efficient Model-Agnostic Multi-Group Equivariant Networkscited by 1
  36. 2024Higher-Order GNNs Meet Efficiency: Sparse Sobolev Graph Neural Networkscited by 1
  37. 2025Diagonal Symmetrization of Neural Network Solvers for the Many-Electron Schr"odinger Equationcited by 1
  38. 2025Piecewise Constant Spectral Graph Neural Networkcited by 1

50 most cited of 72 All 72 (JSON)