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.

References in corpus (2)

• Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states
• Path probability ratios for Langevin dynamics -- exact and approximate

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