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Cormorant: Covariant Molecular Neural Networks

arXiv 1906.04015 ↗First posted 6 Jun 2019physics.comp-ph cs.LG stat.MLcited by 262

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Abstract (arXiv)

We propose Cormorant, a rotationally covariant neural network architecture for learning the behavior and properties of complex many-body physical systems. We apply these networks to molecular systems with two goals: learning atomic potential energy surfaces for use in Molecular Dynamics simulations, and learning ground state properties of molecules calculated by Density Functional Theory. Some of the key features of our network are that (a) each neuron explicitly corresponds to a subset of atoms; (b) the activation of each neuron is covariant to rotations, ensuring that overall the network is fully rotationally invariant. Furthermore, the non-linearity in our network is based upon tensor products and the Clebsch-Gordan decomposition, allowing the network to operate entirely in Fourier space. Cormorant significantly outperforms competing algorithms in learning molecular Potential Energy Surfaces from conformational geometries in the MD-17 dataset, and is competitive with other methods at learning geometric, energetic, electronic, and thermodynamic properties of molecules on the GDB-9 dataset.

Key facts. Cited by 262 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Jun 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 54; 2022: 60; 2023: 55; 2024: 46; 2025: 30; 2026: 17.

262 papers.

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  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  2. 2021E(n) Equivariant Graph Neural Networkscited by 951
  3. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  4. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  5. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  6. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  7. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  8. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  9. 2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
  10. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  11. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  12. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
38 more
  1. 2023Geometric Latent Diffusion Models for 3D Molecule Generationcited by 185
  2. 2022Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pocketscited by 182
  3. 2022Graph neural networks for materials science and chemistrycited by 181
  4. 2022TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentialscited by 179
  5. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  6. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  7. 2021E(n) Equivariant Normalizing Flowscited by 165
  8. 2021Nested Graph Neural Networkscited by 136
  9. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  10. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  11. 2024D-Flow: Differentiating through Flows for Controlled Generationcited by 115
  12. 2021Geometric Deep Learning on Molecular Representationscited by 113
  13. 2021SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effectscited by 103
  14. 2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 100
  15. 2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
  16. 2022One Transformer Can Understand Both 2D & 3D Molecular Datacited by 77
  17. 2021SE(3) Equivariant Graph Neural Networks with Complete Local Framescited by 75
  18. 2021Residual Pathway Priors for Soft Equivariance Constraintscited by 74
  19. 2023A Comprehensive Survey on Deep Graph Representation Learningcited by 72
  20. 2023FAENet: Frame Averaging Equivariant GNN for Materials Modelingcited by 72
  21. 2022ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphscited by 69
  22. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  23. 2021Reconstruction for Powerful Graph Representationscited by 65
  24. 2022GemNet-OC: Developing Graph Neural Networks for Large and Diverse Molecular Simulation Datasetscited by 61
  25. 2022Theory for Equivariant Quantum Neural Networkscited by 60
  26. 2023Equivariant Flow Matching with Hybrid Probability Transportcited by 59
  27. 2022MDM: Molecular Diffusion Model for 3D Molecule Generationcited by 58
  28. 2022Ordered Subgraph Aggregation Networkscited by 57
  29. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 55
  30. 2022Boosting the Cycle Counting Power of Graph Neural Networks with I2-GNNscited by 55
  31. 2022Learning Symmetric Embeddings for Equivariant World Modelscited by 54
  32. 2023Clifford Group Equivariant Neural Networkscited by 54
  33. 2021Equivariant Graph Neural Networks for 3D Macromolecular Structurecited by 53
  34. 2023TensorNet: Cartesian Tensor Representations for Efficient Learning of Molecular Potentialscited by 53
  35. 2021Rotation Invariant Graph Neural Networks using Spin Convolutionscited by 52
  36. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  37. 2022Spherical Channels for Modeling Atomic Interactionscited by 47
  38. 2023Ewald-based Long-Range Message Passing for Molecular Graphscited by 46

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