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Generative models are a promising tool to address the sampling problem inmulti-body and condensed-matter systems in the framework of statisticalmechanics. In this work, we show that normalizing flows can be used to learn atransformation to map different liquid systems into each other allowing at thesame time to obtain an unbiased equilibrium distribution through a reweightingprocess. Two proof-of-principles calculations are presented for thetransformation between Lennard-Jones systems of particles with different depthsof the potential well and for the transformation between a Lennard-Jones and asystem of repulsive particles. In both numerical experiments, systems are inthe liquid state. In future applications, this approach could lead to efficientmethods to simulate liquid systems at ab-initio accuracy with the computationalcost of less accurate models, such as force field or coarse-grainedsimulations.

Learning Mappings between Equilibrium States of Liquid Systems Using Normalizing Flows