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Sampling the phase space of molecular systems -- and, more generally, ofcomplex systems effectively modeled by stochastic differential equations -- isa crucial modeling step in many fields, from protein folding to materialsdiscovery. These problems are often multiscale in nature: they can be describedin terms of low-dimensional effective free energy surfaces parametrized by asmall number of "slow" reaction coordinates; the remaining "fast" degrees offreedom populate an equilibrium measure on the reaction coordinate values.Sampling procedures for such problems are used to estimate effective freeenergy differences as well as ensemble averages with respect to the conditionalequilibrium distributions; these latter averages lead to closures for effectivereduced dynamic models. Over the years, enhanced sampling techniques coupledwith molecular simulation have been developed. An intriguing analogy ariseswith the field of Machine Learning (ML), where Generative Adversarial Networkscan produce high dimensional samples from low dimensional probabilitydistributions. This sample generation returns plausible high dimensional spacerealizations of a model state, from information about its low-dimensionalrepresentation. In this work, we present an approach that couples physics-basedsimulations and biasing methods for sampling conditional distributions withML-based conditional generative adversarial networks for the same task. The"coarse descriptors" on which we condition the fine scale realizations caneither be known a priori, or learned through nonlinear dimensionalityreduction. We suggest that this may bring out the best features of bothapproaches: we demonstrate that a framework that couples cGANs withphysics-based enhanced sampling techniques can improve multiscale SDE dynamicalsystems sampling, and even shows promise for systems of increasing complexity.

GANs and Closures: Micro-Macro Consistency in Multiscale Modeling