mlsanityData to 7 Oct 2026

N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials

arXiv 1803.01588 ↗First posted 5 Mar 2018cs.LG cs.AIcited by 42

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Abstract (arXiv)

We describe N-body networks, a neural network architecture for learning the behavior and properties of complex many body physical systems. Our specific application is to learn atomic potential energy surfaces for use in molecular dynamics simulations. Our architecture is novel in that (a) it is based on a hierarchical decomposition of the many body system into subsytems, (b) the activations of the network correspond to the internal state of each subsystem, (c) the "neurons" in the network are constructed explicitly so as to guarantee that each of the activations is covariant to rotations, (d) the neurons operate entirely in Fourier space, and the nonlinearities are realized by tensor products followed by Clebsch-Gordan decompositions. As part of the description of our network, we give a characterization of what way the weights of the network may interact with the activations so as to ensure that the covariance property is maintained.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Mar 2018.

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Citing papers per year: 2021: 16; 2022: 12; 2023: 1; 2024: 8; 2025: 3; 2026: 2.

42 papers.

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  1. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  2. 2022MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fieldscited by 467
  3. 2022Learning Local Equivariant Representations for Large-Scale Atomistic Dynamicscited by 254
  4. 2021Frame Averaging for Invariant and Equivariant Network Designcited by 166
  5. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  6. 2022The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentialscited by 100
  7. 2025EQ-VAE: Equivariance Regularized Latent Space for Improved Generative Image Modelingcited by 85
  8. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  9. 2021Equivariant Graph Neural Networks for 3D Macromolecular Structurecited by 53
  10. 2021DISCO: accurate Discrete Scale Convolutionscited by 35
  11. 2022Symmetry Group Equivariant Architectures for Physicscited by 23
  12. 2021Rotation-Equivariant Deep Learning for Diffusion MRIcited by 20
30 more
  1. 2022Dimensionless machine learning: Imposing exact units equivariancecited by 16
  2. 2025The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Productscited by 14
  3. 2022Machine learning and invariant theorycited by 13
  4. 2021Equivariant geometric learning for digital rock physics: estimating formation factor and effective permeability tensors from Morse graphcited by 11
  5. 2021Iterative SE(3)-Transformerscited by 10
  6. 2021Geometric Algebra Attention Networks for Small Point Cloudscited by 10
  7. 2023Towards fully covariant machine learningcited by 10
  8. 2024A Characterization Theorem for Equivariant Networks with Point-wise Activationscited by 9
  9. 2021Deformation Robust Roto-Scale-Translation Equivariant CNNscited by 7
  10. 2024Learning local equivariant representations for quantum operatorscited by 7
  11. 2024Relaxed Equivariant Graph Neural Networkscited by 7
  12. 2021A simple equivariant machine learning method for dynamics based on scalarscited by 6
  13. 2021Topos and Stacks of Deep Neural Networkscited by 5
  14. 2022PDO-s3DCNNs: Partial Differential Operator Based Steerable 3D CNNscited by 4
  15. 2021Protein sequence-to-structure learning: Is this the end(-to-end revolution)?cited by 3
  16. 2022Unifying O(3) Equivariant Neural Networks Design with Tensor-Network Formalismcited by 3
  17. 2024ILPO-NET: Network for the invariant recognition of arbitrary volumetric patterns in 3Dcited by 3
  18. 2024Tensor learning with orthogonal, Lorentz, and symplectic symmetriescited by 3
  19. 20216DCNN with roto-translational convolution filters for volumetric data processingcited by 2
  20. 2022A Feedforward Unitary Equivariant Neural Networkcited by 2
  21. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  22. 2022Group-invariant tensor train networks for supervised learningcited by 1
  23. 2022Equivalence Between SE(3) Equivariant Networks via Steerable Kernels and Group Convolutioncited by 1
  24. 2024On the Fourier analysis in the SO(3) space : EquiLoPO Networkcited by 1
  25. 2025Learning from Frustration: Torsor CNNs on Graphscited by 1
  26. 2021Flexible dual-branched message passing neural network for quantum mechanical property prediction with molecular conformationcited by 0
  27. 2022Design equivariant neural networks for 3D point cloudcited by 0
  28. 2024Adaptive Sampling for Continuous Group Equivariant Neural Networkscited by 0
  29. 2026Warm-starting PDE solvers with any-dimensional machine learningcited by 0
  30. 2026NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learningcited by 0