The geometry of generalized force matching and related information metrics in coarse-graining of molecular systems.
Using the probabilistic language of conditional expectations, we reformulate the force matching method for coarse-graining of molecular systems as a projection onto 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 and 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.
Department of Mathematics and Applied Mathematics, University of Crete, 70013 Heraklion, Greece.
Evangelia
E
Kalligiannaki
Department of Mathematics and Applied Mathematics, University of Crete, 70013 Heraklion, Greece.
Vagelis
V
Harmandaris
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Markos A
MA
Katsoulakis
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, USA.
Petr
P
Plecháč
D019277:Entropy; D056004:Molecular Dynamics Simulation; D009010:Monte Carlo Method