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.
@article{arxiv.1910.00753,
title = {Equivariant Flows: sampling configurations for multi-body systems with symmetric energies},
author = {Jonas Köhler and Leon Klein and Frank Noé},
journal= {arXiv preprint arXiv:1910.00753},
year = {2019}
}