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

Abstract

In this paper we discuss information-theoretic tools for obtaining optimized coarse-grained molecular models for both equilibrium and non-equilibrium molecular simulations. 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 models 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. We demonstrate the enhanced transferability of information-based parameterizations to different observables, at a specific thermodynamic point, due to information inequalities.We 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 overdamped and driven Langevin dynamics of interacting particles.

From Atomistic to Systematic Coarse-Grained Models for Molecular Systems

“…In addition, non-linear CG maps could be also relevant especially when free energy differences, such as in thermodynamic integration, are to be computed. Parametrization of the dynamics of CG models is also one of the most challenging issues, in particular for non-equilibrium molecular systems [3,24,5,25].…”

“…This retrieves the relation of the path-space force matching approach to the diffusion coefficient of the atomistic dynamics. Moreover, if we assume e equilibrium dynamics and constant diffusion (x) = the optimization problem is reduced to the known FM method, see also Remark 6.3 in [5],…”

“…Methods such as inverse Monte Carlo [1], inverse Boltzmann [2], force matching [3], relative entropy [4], provide parameterizations of coarse-grained effective potentials at equilibrium by minimizing a fitting functional over a parameter space. Then, we further extend these studies using path-space methods (relative entropy rate) for coarse-graining and uncertainty quantification for non-equilibrium processes, [5,6,7,8].…”

“…We present two main results of our latest studies, [9,5]. Firstly, on optimizing coarse-grained models in equilibrium, we: (a) reveal the connection of the force matching method with thermodynamic integration.…”

Special Issue: Big data and predictive computational modeling

“…Model-selection issues arise prominently in obtaining reduced or coarse-grained descriptions of physical models (e.g., in molecular dynamics or quantum mechanical models), and along these lines the expertise and arsenal of tools from machine learning/computational statistics can be extremely powerful [10,3,4]. Informationtheoretic tools and pertinent concepts can be extremely useful [9].…”