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

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.

References in corpus (5)

• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Sensitivity, robustness and identifiability in stochastic chemical kinetics models
• Examination of the concept of degree of rate control by first-principles kinetic Monte Carlo simulations
• An efficient sampling algorithm for Variational Monte Carlo
• Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

Cited by in corpus (13)

• Information-theoretic tools for parametrized coarse-graining of non-equilibrium extended systems
• Path-space variational inference for non-equilibrium coarse-grained systems
• Scalable Information Inequalities for Uncertainty Quantification
• A practical approach to the sensitivity analysis for kinetic Monte Carlo simulation of heterogeneous catalysis
• Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations
• Causality and Bayesian network PDEs for multiscale representations of porous media
• Mutual Information for Explainable Deep Learning of Multiscale Systems
• Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks
• Efficient estimators for likelihood ratio sensitivity indices of complex stochastic dynamics
• Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities
• Uncertainty quantification for generalized Langevin dynamics
• Parallel replica dynamics method for bistable stochastic reaction networks: simulation and sensitivity analysis
• Information Criteria for quantifying loss of reversibility in parallelized KMC