Equivariant Flows: sampling configurations for multi-body systems with symmetric energies
This addresses the challenge of scaling generative models for complex physical systems, offering a domain-specific improvement for computational physics and molecular dynamics.
The paper tackles the problem of sampling equilibrium states of many-body systems like proteins by developing equivariant flows that incorporate symmetries of the energy function, resulting in a Boltzmann Generator that generalizes to new configurations where non-equivariant methods fail.
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.