Parametric Sensitivity Analysis for Stochastic Molecular Systems using Information Theoretic Metrics

TL;DR

This paper extends parametric sensitivity analysis to stochastic molecular systems using information-theoretic metrics, enabling efficient sensitivity computation from single simulations in both equilibrium and non-equilibrium regimes.

Contribution

It introduces a pathwise sensitivity analysis method based on relative entropy rate and Fisher information matrix for stochastic differential equations in molecular dynamics.

Findings

RER-based sensitivities correlate well with observable sensitivities

Method applicable to equilibrium and non-equilibrium steady states

Validated on Lennard-Jones fluid and methane liquid

Abstract

In this paper we extend the parametric sensitivity analysis (SA) methodology proposed in Ref. [Y. Pantazis and M. A. Katsoulakis, J. Chem. Phys. 138, 054115 (2013)] to continuous time and continuous space Markov processes represented by stochastic differential equations and, particularly, stochastic molecular dynamics as described by the Langevin equation. The utilized SA method is based on the computation of the information-theoretic (and thermodynamic) quantity of relative entropy rate (RER) and the associated Fisher information matrix (FIM) between path distributions. A major advantage of the pathwise SA method is that both RER and pathwise FIM depend only on averages of the force field therefore they are tractable and computable as ergodic averages from a single run of the molecular dynamics simulation both in equilibrium and in non-equilibrium steady state regimes. We validate the performance of the extended SA method to two different molecular stochastic systems, a standard Lennard-Jones fluid and an all-atom methane liquid and compare the obtained parameter sensitivities with parameter sensitivities on three popular and well-studied observable functions, namely, the radial distribution function, the mean squared displacement and the pressure. Results show that the RER-based sensitivities are highly correlated with the observable-based sensitivities.