A new stochastic mode reduction strategy for dissipative systems

TL;DR

This paper introduces a novel stochastic mode reduction method for dissipative systems, combining renormalization group techniques with maximum entropy principles to achieve efficient, rigorous dimension reduction and universal long-term behavior characterization.

Contribution

It develops a new stochastic mode reduction strategy for dissipative systems using an information theoretic extension of renormalization group methods, providing a rigorous and computationally efficient approach.

Findings

The reduced model accurately captures the long-time behavior of the system.

The fast modes follow a universal distribution independent of initial conditions.

Numerical results support the theoretical derivation of the stochastic process.

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.