A review of Girsanov reweighting and of square root approximation for building molecular Markov state models

Abstract

Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential ̃V(x) from trajectories that have been generated at a different potential V(x). In this article, we present Girsanov reweighting and square root approxi- mation: the first method reweights path probabilities exploiting the Girsanov theorem and can be applied to Markov state models to reweight transition probabilities; the second method was originally developed to discretize the Fokker–Planck operator into a transition rate matrix, but here we implement it into a reweighting scheme for transition rates. We begin by reviewing the theoretical background of the methods and then present two applications relevant to molecular dynamics, highlighting their strengths and weaknesses.