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 $\tilde{V}(x)$ 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.

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Cited by in corpus (2)

• Spectral Map for Slow Collective Variables, Markovian Dynamics, and Transition State Ensembles
• Tensor-SqRA: Modeling the Transition Rates of Interacting Molecular Systems in terms of Potential Energies