mlsanityData to 7 Oct 2026

Equivariant message passing for the prediction of tensorial properties and molecular spectra

arXiv 2102.03150 ↗First posted 5 Feb 2021cs.LG physics.chem-phcited by 438

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Cited by 20 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Message passing neural networks have become a method of choice for learning on graphs, in particular the prediction of chemical properties and the acceleration of molecular dynamics studies. While they readily scale to large training data sets, previous approaches have proven to be less data efficient than kernel methods. We identify limitations of invariant representations as a major reason and extend the message passing formulation to rotationally equivariant representations. On this basis, we propose the polarizable atom interaction neural network (PaiNN) and improve on common molecule benchmarks over previous networks, while reducing model size and inference time. We leverage the equivariant atomwise representations obtained by PaiNN for the prediction of tensorial properties. Finally, we apply this to the simulation of molecular spectra, achieving speedups of 4-5 orders of magnitude compared to the electronic structure reference.

Key facts. Cited by 438 papers in the map (data through 7 Oct 2026). Builds on 30 of its 70 references that are in the map. First posted on arXiv 5 Feb 2021.

Builds on

30 of 70 references.

References · 30

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  4. 2015Convolutional Networks on Graphs for Learning Molecular Fingerprintscited by 751
  5. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  6. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  7. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  8. 2020Directional Message Passing for Molecular Graphscited by 556
  9. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  10. 2020Learning from Protein Structure with Geometric Vector Perceptronscited by 308
  11. 2016Steerable CNNscited by 298
  12. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
18 more
  1. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  2. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  3. 2016Molecular Graph Convolutions: Moving Beyond Fingerprintscited by 238
  4. 2020Machine Learning Force Fieldscited by 204
  5. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 193
  6. 2017Graph Embedding Techniques, Applications, and Performance: A Surveycited by 188
  7. 2019Symmetry-adapted generation of 3d point sets for the targeted discovery of moleculescited by 171
  8. 2019Deep neural network solution of the electronic Schr"odinger equationcited by 124
  9. 2019Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctionscited by 73
  10. 2018CubeNet: Equivariance to 3D Rotation and Translationcited by 59
  11. 2019Equivariant Flows: sampling configurations for multi-body systems with symmetric energiescited by 57
  12. 2020Symmetry-Aware Actor-Critic for 3D Molecular Designcited by 55
  13. 2020Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Propertiescited by 51
  14. 2017Hierarchical modeling of molecular energies using a deep neural networkcited by 37
  15. 2017Machine Learning Molecular Dynamics for the Simulation of Infrared Spectracited by 30
  16. 2020Predicting molecular dipole moments by combining atomic partial charges and atomic dipolescited by 18
  17. 202086 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracycited by 15
  18. 2020Combining SchNet and SHARC: The SchNarc machine learning approach for excited-state dynamicscited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 23; 2022: 68; 2023: 86; 2024: 93; 2025: 90; 2026: 78.

438 papers.

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  1. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  2. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  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. 2022Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pocketscited by 182
  8. 2022Graph neural networks for materials science and chemistrycited by 181
  9. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
  10. 2022e3nn: Euclidean Neural Networkscited by 171
  11. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  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. 2021Geometric Deep Learning on Molecular Representationscited by 113
  4. 2023Reducing SO(3) Convolutions to SO(2) for Efficient Equivariant GNNscited by 113
  5. 2021GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensemblescited by 106
  6. 2021SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effectscited by 103
  7. 2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 100
  8. 2022The Open Catalyst 2022 (OC22) Dataset and Challenges for Oxide Electrocatalystscited by 95
  9. 2021Inverse design of 3d molecular structures with conditional generative neural networkscited by 93
  10. 2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 92
  11. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  12. 2023Attending to Graph Transformerscited by 81
  13. 2022SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentialscited by 80
  14. 2025Learning Smooth and Expressive Interatomic Potentials for Physical Property Predictioncited by 79
  15. 2022One Transformer Can Understand Both 2D & 3D Molecular Datacited by 77
  16. 2023A Comprehensive Survey on Deep Graph Representation Learningcited by 72
  17. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 72
  18. 2022ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphscited by 69
  19. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  20. 2022Molecular Geometry Pretraining with SE(3)-Invariant Denoising Distance Matchingcited by 67
  21. 2022MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Designcited by 66
  22. 2023A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systemscited by 65
  23. 2022GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasetscited by 61
  24. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  25. 2023Clifford Group Equivariant Neural Networkscited by 54
  26. 2021Equivariant Graph Neural Networks for 3D Macromolecular Structurecited by 53
  27. 2023TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentialscited by 53
  28. 2025Position: Graph Learning Will Lose Relevance Due To Poor Benchmarkscited by 52
  29. 2023Navigating the Design Space of Equivariant Diffusion-Based Generative Models for De Novo 3D Molecule Generationcited by 50
  30. 2022Spherical Channels for Modeling Atomic Interactionscited by 47
  31. 2023Ewald-based Long-Range Message Passing for Molecular Graphscited by 46
  32. 2023A new perspective on building efficient and expressive 3D equivariant graph neural networkscited by 46
  33. 2022Unified 2D and 3D Pre-Training of Molecular Representationscited by 45
  34. 2021Molformer: Motif-based Transformer on 3D Heterogeneous Molecular Graphscited by 44
  35. 2024Transferable Boltzmann Generatorscited by 43
  36. 2023MUDiff: Unified Diffusion for Complete Molecule Generationcited by 41
  37. 2024ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generationcited by 41
  38. 2022So3krates: Equivariant attention for interactions on arbitrary length-scales in molecular systemscited by 39

50 most cited of 438 All 438 (JSON)