N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials
This work addresses the challenge of accurately modeling complex many-body physical systems for molecular dynamics simulations, representing an incremental improvement with a novel architectural approach.
The authors tackled the problem of learning atomic potential energy surfaces for molecular dynamics by introducing N-body networks, a covariant hierarchical neural network architecture that decomposes many-body systems into subsystems and ensures rotational covariance through Fourier-space operations and Clebsch-Gordan decompositions, achieving results that guarantee covariance properties without specific numerical performance metrics.
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.