Dimension reduction for systems with slow relaxation
Statistical Mechanics
2017-05-24 v2 Probability
Data Analysis, Statistics and Probability
Abstract
We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.
Cite
@article{arxiv.1609.09222,
title = {Dimension reduction for systems with slow relaxation},
author = {Shankar C. Venkataramani and Raman C. Venkataramani and Juan M. Restrepo},
journal= {arXiv preprint arXiv:1609.09222},
year = {2017}
}
Comments
48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanoff