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.
@article{arxiv.1305.4135,
title = {A new stochastic mode reduction strategy for dissipative systems},
author = {M. Schmuck and M. Pradas and S. Kalliadasis and G. A. Pavliotis},
journal= {arXiv preprint arXiv:1305.4135},
year = {2013}
}