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A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics
Yannis Pantazis1, Markos A Katsoulakis
1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-9305, USA.
The Journal of Chemical Physics
|February 15, 2013
Summary
We introduce a novel sensitivity analysis method for complex stochastic dynamics using relative entropy rate. This approach is computationally feasible in the stationary regime and handles challenging systems like non-equilibrium and high-dimensional models.
Area of Science:
- Computational Physics
- Statistical Mechanics
- Dynamical Systems Theory
Background:
- Sensitivity analysis is crucial for understanding complex stochastic dynamics.
- Traditional methods struggle with non-Gaussian distributions, metastability, and high dimensionality.
- Analyzing non-equilibrium and complex landscape systems remains a significant challenge.
Purpose of the Study:
- To develop a computationally feasible sensitivity analysis methodology for complex stochastic dynamics.
- To enable analysis of systems with non-Gaussian stationary distributions and high dimensionality.
- To provide a robust framework for studying non-equilibrium and metastable systems.
Main Methods:
- The proposed method is based on the relative entropy rate and Fisher information matrix.
- It operates in the stationary regime, calculating observables in path space.
- Direct Monte Carlo simulation of derived observables bypasses the need for explicit probability distributions.
Main Results:
- The methodology is demonstrated on Langevin particle systems (reversible and non-reversible forcing).
- It successfully performs sensitivity analysis on non-equilibrium systems.
- The method is applied to high-dimensional, spatially extended kinetic Monte Carlo models.
Conclusions:
- The new sensitivity analysis method is effective for complex stochastic dynamics.
- It overcomes limitations of traditional approaches for non-Gaussian and high-dimensional systems.
- The methodology offers a powerful tool for analyzing non-equilibrium and metastable systems.
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