Equivariant Flows: sampling configurations for multi-body systems with symmetric energies

TL;DR

This paper introduces equivariant flow models that incorporate physical symmetries into generative neural networks, enabling more effective sampling of complex many-body systems like proteins.

Contribution

It develops theoretical methods for constructing equivariant flows and demonstrates their ability to generalize better in sampling tasks involving symmetric energies.

Findings

Equivariant flows improve sampling of symmetric physical systems.

Equivariant Boltzmann Generators can generate new configurations beyond non-equivariant models.

Theoretical tools for symmetry-aware flow construction are proposed.

Abstract

Flows are exact-likelihood generative neural networks that transform samples from a simple prior distribution to the samples of the probability distribution of interest. Boltzmann Generators (BG) combine flows and statistical mechanics to sample equilibrium states of strongly interacting many-body systems such as proteins with 1000 atoms. In order to scale and generalize these results, it is essential that the natural symmetries of the probability density - in physics defined by the invariances of the energy function - are built into the flow. Here we develop theoretical tools for constructing such equivariant flows and demonstrate that a BG that is equivariant with respect to rotations and particle permutations can generalize to sampling nontrivially new configurations where a nonequivariant BG cannot.