Path space force matching and relative entropy methods for coarse-graining molecular systems at transient regimes

Data-driven coarse-graining is the point of view of many scientists over the past decades for studying mesoscale properties of complex molecular systems. So far, there is a good understanding of the coarse-graining of systems at equilibrium conditions with thorough literature devoted to the subject. On the other hand, to extract effective dynamics of the reduced system is non-trivial and in general computationally costly. Information theoretic tools for coarse-graining extended systems were developed and analyzed in our recent works for systems at and out-of-equilibrium. In the current work we present the theory of path space force matching and relative entropy methods, at continuous time. We present the details of the numerical implementation for force matching and the path space force matching. We are able for the first time to benchmark and validate the path space force matching through its the application for a liquid methane system, at the equilibrium regime as well as at the transient regime. (C) 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by/nc-nd/3.0/) Peer-review under responsibility of the scientific committee of the 7th International Young Scientist Conference on Computational Science.