Path-space variational inference for non-equilibrium coarse-grained systems

In this paper, we discuss information-theoretic tools for obtaining optimized coarse-grained molecular models for both equilibrium and non-equilibrium molecular dynamics. The latter are ubiquitous in physicochemical and biological applications, where they are typically associated with coupling mechanisms, multi-physics and/or boundary conditions. In general the non-equilibrium steady states are not known explicitly as they do not necessarily have a Gibbs structure. The presented approach can compare microscopic behavior of molecular systems to parametric and non-parametric coarse-grained one using the relative entropy between distributions on the path space and setting up a corresponding path space variational inference problem. The methods can become entirely data-driven when the microscopic dynamics are replaced with corresponding correlated data in the form of time series. Furthermore, we present connections and generalizations of force matching methods in coarse-graining with path-space information methods, as well as demonstrate the enhanced transferability of information-based parameterizations to general observables due to information inequalities. We further discuss methodological connections between information-based coarse-graining of molecular systems and variational inference methods primarily developed in the machine learning community. However, we note that the work presented here addresses variational inference for correlated time series due to the focus on dynamics. The applicability of the proposed methods is demonstrated on high-dimensional stochastic processes given by Langevin, overdamped and driven Langevin dynamics of interacting particles.