The geometry of generalized force matching in coarse-graining and related information metrics
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2015
- DOI:
- 10.48550/arXiv.1504.02152
- arXiv:
- arXiv:1504.02152
- Bibcode:
- 2015arXiv150402152K
- Keywords:
-
- Mathematics - Numerical Analysis;
- Physics - Chemical Physics