Parametric sensitivity analysis for stochastic molecular systems using information theoretic metrics

Abstract

In this paper, we present a parametric sensitivity analysis (SA) methodology for continuous time and continuous space Markov processes represented by stochastic differential equations. Particularly, we focus on 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, and it is an extension of the work proposed by Y. Pantazis and M. A. Katsoulakis [J. Chem. Phys. 138, 054115 (2013)]. 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.

Robust Information Divergences for Model-Form Uncertainty Arising from Sparse Data in Random PDE

“…when considering small perturbations to a smooth parametric family of probability measures; the complete proof follows from results in [21]. A similar linearization has been used in chemical kinetics to screen for insensitive parameter directions in the situation where the number of parameters is large ( [3,56]). For both a multivariate normal distribution and log-normal distribution characterized by mean µ(θ) and covariance Σ(θ), the i, j component of FIM can be expressed as…”

Girsanov reweighting for path ensembles and Markov state models

“…Similarly, one can use Girsanov reweighting to understand the influence of restraining potentials 50,51 on the dynamics of the system. Second, the method can be used to understand which degrees of freedom have the largest influence on the slow modes of the molecule 52,53 . For example, for alanine dipeptide, we showed that the slow dynamic modes are more sensitive to a force field variation in the φ-backbone dihedral angle than they are to a variation in the ψ-backbone dihedral angle.…”

Pathwise Sensitivity Analysis in Transient Regimes

“…We finally remark that a popular method for modeling non-equilibrium systems in atomistic and mesoscopic scales is based on the Langevin equation. Langevin equation is a degenerate system of stochastic differential equations whose sensitivity analysis based on the relative entropy rate and the associated pathwise FIM was performed in [25].…”