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We propose a new sensitivity analysis methodology for complex stochasticdynamics based on the Relative Entropy Rate. The method becomes computationallyfeasible at the stationary regime of the process and involves the calculationof suitable observables in path space for the Relative Entropy Rate and thecorresponding Fisher Information Matrix. The stationary regime is crucial forstochastic dynamics and here allows us to address the sensitivity analysis ofcomplex systems, including examples of processes with complex landscapes thatexhibit metastability, non-reversible systems from a statistical mechanicsperspective, and high-dimensional, spatially distributed models. All thesesystems exhibit, typically non-gaussian stationary probability distributions,while in the case of high-dimensionality, histograms are impossible toconstruct directly. Our proposed methods bypass these challenges relying on thedirect Monte Carlo simulation of rigorously derived observables for theRelative Entropy Rate and Fisher Information in path space rather than on thestationary probability distribution itself. We demonstrate the capabilities ofthe 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 outsensitivity analysis in non-equilibrium systems; and, (b) spatially extendedKinetic Monte Carlo models, showing that the method can handle high-dimensionalproblems.

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