mlsanityData to 7 Oct 2026

GemNet: Universal Directional Graph Neural Networks for Molecules

arXiv 2106.08903 ↗First posted 2 Jun 2021physics.comp-ph cs.LG physics.chem-phcited by 342

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Abstract (arXiv)

Effectively predicting molecular interactions has the potential to accelerate molecular dynamics by multiple orders of magnitude and thus revolutionize chemical simulations. Graph neural networks (GNNs) have recently shown great successes for this task, overtaking classical methods based on fixed molecular kernels. However, they still appear very limited from a theoretical perspective, since regular GNNs cannot distinguish certain types of graphs. In this work we close this gap between theory and practice. We show that GNNs with spherical representations are indeed universal approximators for predictions that are invariant to translation, and equivariant to permutation and rotation. We then discretize such GNNs via directed edge embeddings and two-hop message passing, and incorporate multiple structural improvements to arrive at the geometric message passing neural network (GemNet). We demonstrate the benefits of the proposed changes in multiple ablation studies. GemNet outperforms previous models on the COLL, MD17, and OC20 datasets by 34%, 41%, and 20%, respectively, and performs especially well on the most challenging molecules. Our implementation is available online.

Key facts. Cited by 342 papers in the map (data through 7 Oct 2026). Builds on 39 of its 67 references that are in the map. First posted on arXiv 2 Jun 2021.

Builds on

39 of 67 references.

References · 39

  1. 2018How Powerful are Graph Neural Networks?cited by 4,355
  2. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  3. 2016Group Equivariant Convolutional Networkscited by 1,154
  4. 2017Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learningcited by 935
  5. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 878
  6. 2019On the Convergence of Adam and Beyondcited by 834
  7. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  8. 2018PointConv: Deep Convolutional Networks on 3D Point Cloudscited by 656
  9. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  10. 2017Self-Normalizing Neural Networkscited by 591
  11. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  12. 2020Directional Message Passing for Molecular Graphscited by 556
27 more
  1. 2018Spherical CNNscited by 452
  2. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  3. 2019Provably Powerful Graph Networkscited by 385
  4. 2021High-Performance Large-Scale Image Recognition Without Normalizationcited by 359
  5. 2018How Does Batch Normalization Help Optimization?cited by 355
  6. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  7. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  8. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  9. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  10. 2020The Open Catalyst 2020 (OC20) Dataset and Community Challengescited by 246
  11. 2017Learning SO(3) Equivariant Representations with Spherical CNNscited by 244
  12. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  13. 2020Generalization and Representational Limits of Graph Neural Networkscited by 217
  14. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 168
  15. 2019On the Universality of Invariant Networkscited by 151
  16. 2018Universal approximations of invariant maps by neural networkscited by 127
  17. 2020Lorentz Group Equivariant Neural Network for Particle Physicscited by 120
  18. 2020Expressive Power of Invariant and Equivariant Graph Neural Networkscited by 100
  19. 2020On Learning Sets of Symmetric Elementscited by 97
  20. 2021Characterizing signal propagation to close the performance gap in unnormalized ResNetscited by 87
  21. 2020On the Universality of Rotation Equivariant Point Cloud Networkscited by 80
  22. 2020OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Featurescited by 63
  23. 2021ForceNet: A Graph Neural Network for Large-Scale Quantum Calculationscited by 58
  24. 2018Towards Understanding Regularization in Batch Normalizationcited by 56
  25. 2018Covariant Compositional Networks For Learning Graphscited by 54
  26. 2020Spin-Weighted Spherical CNNscited by 50
  27. 2020Neural Message Passing on High Order Pathscited by 17

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 9; 2022: 62; 2023: 91; 2024: 68; 2025: 65; 2026: 47.

342 papers.

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  1. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  2. 2021Crystal Diffusion Variational Autoencoder for Periodic Material Generationcited by 268
  3. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  4. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  5. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  6. 2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
  7. 2022Graph neural networks for materials science and chemistrycited by 181
  8. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  9. 2022Protein Representation Learning by Geometric Structure Pretrainingcited by 161
  10. 20213D Infomax improves GNNs for Molecular Property Predictioncited by 146
  11. 2023Crystal Structure Prediction by Joint Equivariant Diffusioncited by 142
  12. 2023Equivariant flow matchingcited by 131
38 more
  1. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  2. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  3. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  4. 2022Generating 3D Molecules for Target Protein Bindingcited by 104
  5. 2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 100
  6. 2023MatterGen: a generative model for inorganic materials designcited by 98
  7. 2023MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generationcited by 96
  8. 2022The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalystscited by 95
  9. 2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 92
  10. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  11. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  12. 2023Attending to Graph Transformerscited by 81
  13. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 79
  14. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 72
  15. 2022ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphscited by 69
  16. 2022Molecular Geometry Pretraining with SE(3)-Invariant Denoising Distance Matchingcited by 67
  17. 2022MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Designcited by 66
  18. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  19. 2022GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasetscited by 61
  20. 2022Ordered Subgraph Aggregation Networkscited by 57
  21. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  22. 2023Clifford Group Equivariant Neural Networkscited by 54
  23. 2023How does over-squashing affect the power of GNNs?cited by 53
  24. 2023TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentialscited by 53
  25. 2022Graph-based Molecular Representation Learningcited by 51
  26. 2022Spherical Channels for Modeling Atomic Interactionscited by 47
  27. 2023Ewald-based Long-Range Message Passing for Molecular Graphscited by 46
  28. 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 46
  29. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 46
  30. 2024Transferable Boltzmann Generatorscited by 43
  31. 2023Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Spacecited by 40
  32. 2024The Importance of Being Scalable: Improving the Speed and Accuracy of Neural Network Interatomic Potentials Across Chemical Domainscited by 40
  33. 2022So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systemscited by 39
  34. 2023Smooth, exact rotational symmetrization for deep learning on point cloudscited by 39
  35. 2023From Molecules to Materials: Pre-training Large Generalizable Models for Atomic Property Predictioncited by 39
  36. 2023Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltoniancited by 38
  37. 2022SpeqNets: Sparsity-aware Permutation-equivariant Graph Networkscited by 37
  38. 2023Efficient Approximations of Complete Interatomic Potentials for Crystal Property Predictioncited by 37

50 most cited of 342 All 342 (JSON)