Learning mappings between equilibrium states of liquid systems using normalizing flows

Generative models and, in particular, normalizing flows are a promising tool in statistical mechanics to address the sampling problem in condensed-matter systems. In this work, we investigate the potential of normalizing flows to learn a transformation to map different liquid systems into each other while allowing at the same time to obtain an unbiased equilibrium distribution. We apply this methodology to the mapping of a small system of fully repulsive disks modeled via the Weeks-Chandler-Andersen potential into a Lennard-Jones system in the liquid phase at different coordinates in the phase diagram. We obtain an improvement in the relative effective sample size of the generated distribution up to a factor of six compared to direct reweighting. We show that this factor can have a strong dependency on the thermodynamic parameters of the source and target system.