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

2018/03/05 by Risi Kondor, Kondor, Risi · 7 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · Physics and Astronomy · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning in Materials Science #Protein Structure and Dynamics #Quantum many-body systems #cs.AI #cs.LG

paper · pdf · doi:10.48550/arxiv.1803.01588

arxiv created 2018/03/05 · openalex publication_date 2018/03/05 · arxiv updated 2018/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Constructing high‐dimensional neural network potentials: A tutorial review
• Learning Convolutional Neural Networks for Graphs
• Covariant Compositional Networks For Learning Graphs
• On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups

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• Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning

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