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

L. Donati, M. Weber, B. G. Keller – 2022

Dynamical reweighting methods permit to estimate kinetic observables of a stochastic process governed by a target potential 𝑉̃(𝑥) from trajectories that have been generated at a different potential V(x). In this article, we present Girsanov reweighting and square root approximation: 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.

Title
A review of Girsanov reweighting and of square root approximation for building molecular Markov state models
Author
L. Donati, M. Weber, B. G. Keller
Date
2022
Identifier
https://doi.org/10.1063/5.0127227
Citation
J. Math. Phys. 63, 123306 (2022)
Type
Text