  Coarse-grained (CG) molecular simulations have become a standard tool to
study molecular processes on time- and length-scales inaccessible to all-atom
simulations. Parameterizing CG force fields to match all-atom simulations has
mainly relied on force-matching or relative entropy minimization, which require
many samples from costly simulations with all-atom or CG resolutions,
respectively. Here we present flow-matching, a new training method for CG force
fields that combines the advantages of both methods by leveraging normalizing
flows, a generative deep learning method. Flow-matching first trains a
normalizing flow to represent the CG probability density, which is equivalent
to minimizing the relative entropy without requiring iterative CG simulations.
Subsequently, the flow generates samples and forces according to the learned
distribution in order to train the desired CG free energy model via force
matching. Even without requiring forces from the all-atom simulations,
flow-matching outperforms classical force-matching by an order of magnitude in
terms of data efficiency, and produces CG models that can capture the folding
and unfolding transitions of small proteins.
