A new stochastic mode reduction strategy for dissipative systems

Abstract

We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally reduced description for such systems. The neglected degrees of freedom by this reduction are replaced by a systematically deefined stochastic process under a constraint on the second moment. This then forms the basis of a computationally efficient method. Numerical computations for the generalized Kuramoto-Sivashinsky equation sup- port our method and reveal that the long-time underlying stochastic process of the fast (unresolved) modes obeys a universal distribution which does not depend on the initial conditions and which we rigorously derive by the maximum entropy principle.

References in corpus (3)

• Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinsky equation
• Additive noise effects in active nonlinear spatially extended systems
• New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials

Cited by in corpus (2)

• Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation
• A new framework for extracting coarse-grained models from time series with multiscale structure