A review of Girsanov Reweighting and of Square Root Approximation for building molecular Markov State Models

TL;DR

This paper reviews Girsanov reweighting and Square Root Approximation methods for estimating kinetic properties of molecular systems, demonstrating their theoretical basis and applications in Molecular Dynamics reweighting schemes.

Contribution

It introduces and compares Girsanov reweighting and SqRA methods for reweighting Markov State Models in molecular simulations, highlighting their theoretical foundations and practical applications.

Findings

Girsanov reweighting effectively reweights transition probabilities in MSMs.

SqRA provides a discretization scheme for the Fokker-Planck operator in reweighting.

Both methods have specific strengths and limitations in MD applications.

Abstract

Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential $\tilde{V}(x)$ from trajectories that have been generated at a different potential $V(x)$. In this article, we present Girsanov reweighting and Square Root Approximation (SqRA): the first method reweights path probabilities exploiting the Girsanov theorem and can be applied to Markov State Models (MSMs) 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, then present two applications relevant to Molecular Dynamics (MD), highlighting their strengths and weaknesses.