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

Jonas Köhler, Leon Klein, Frank Noe

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.