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

TL;DR

This paper introduces N-body networks, a hierarchical neural architecture that models atomic potentials with covariant properties, operating in Fourier space to accurately simulate complex many-body physical systems.

Contribution

The paper presents a novel hierarchical neural network architecture that guarantees rotational covariance and operates in Fourier space for learning atomic potential energy surfaces.

Findings

Successfully models atomic potential energy surfaces.

Ensures covariance through explicit neural construction.

Operates entirely in Fourier space for efficiency.

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.