A Relative Entropy Rate Method for Path Space Sensitivity Analysis of Stationary Complex Stochastic Dynamics

TL;DR

This paper introduces a novel sensitivity analysis method for complex stochastic systems using the Relative Entropy Rate, enabling analysis at the stationary regime without requiring explicit stationary distributions, suitable for high-dimensional and non-equilibrium systems.

Contribution

The paper develops a new path space sensitivity analysis approach based on Relative Entropy Rate, applicable to complex, high-dimensional, and non-reversible stochastic dynamics at stationarity.

Findings

Effective sensitivity analysis for non-reversible systems.

Applicable to high-dimensional spatial models.

Handles non-Gaussian stationary distributions.

Abstract

We propose a new sensitivity analysis methodology for complex stochastic dynamics based on the Relative Entropy Rate. The method becomes computationally feasible at the stationary regime of the process and involves the calculation of suitable observables in path space for the Relative Entropy Rate and the corresponding Fisher Information Matrix. The stationary regime is crucial for stochastic dynamics and here allows us to address the sensitivity analysis of complex systems, including examples of processes with complex landscapes that exhibit metastability, non-reversible systems from a statistical mechanics perspective, and high-dimensional, spatially distributed models. All these systems exhibit, typically non-gaussian stationary probability distributions, while in the case of high-dimensionality, histograms are impossible to construct directly. Our proposed methods bypass these challenges relying on the direct Monte Carlo simulation of rigorously derived observables for the Relative Entropy Rate and Fisher Information in path space rather than on the stationary probability distribution itself. We demonstrate the capabilities of the proposed methodology by focusing here on two classes of problems: (a) Langevin particle systems with either reversible (gradient) or non-reversible (non-gradient) forcing, highlighting the ability of the method to carry out sensitivity analysis in non-equilibrium systems; and, (b) spatially extended Kinetic Monte Carlo models, showing that the method can handle high-dimensional problems.