The geometry of generalized force matching in coarse-graining and related information metrics

TL;DR

This paper reformulates force matching in molecular coarse-graining using probabilistic methods, linking it to thermodynamic integration and extending it to non-linear mappings for improved potential approximation.

Contribution

It introduces a generalized force matching condition applicable to both linear and non-linear coarse graining, and explores its equivalence with relative entropy minimization.

Findings

Provides a probabilistic framework linking force matching and thermodynamic integration.

Extends force matching to non-linear coarse graining mappings.

Demonstrates the approach with molecular system examples.

Abstract

Using the probabilistic language of conditional expectations we reformulate the force matching method for coarse-graining of molecular systems as a projection on spaces of coarse observables. A practical outcome of this probabilistic description is the link of the force matching method with thermodynamic integration. This connection provides a way to systematically construct a local mean force in order to optimally approximate the potential of mean force through force matching. We introduce a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (e.g., reaction coordinates, end-to-end length of chains). Furthermore, we study the equivalence of force matching with relative entropy minimization which we derive for general non-linear coarse graining maps. We present in detail the generalized force matching condition through applications to specific examples in molecular systems.