Dimension reduction for systems with slow relaxation

TL;DR

The paper introduces new methods for reducing complex, slow-relaxing dynamical systems into simpler models, with applications to oil spill evaporation, enhancing understanding of long-term behavior.

Contribution

It develops a mathematical framework and introduces universal and asymptotic filters for optimal model reduction of slow, dissipative systems.

Findings

Effective reduced models for slow relaxation systems

Application to oil spill evaporation modeling

Introduction of universal and asymptotic filters

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.