Dimension reduction for systems with slow relaxation

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.

48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanoff

References in corpus (6)

• Applied Koopmanism
• The sloppy model universality class and the Vandermonde matrix
• Data-driven non-Markovian closure models
• A discrete approach to stochastic parametrization and dimensional reduction in nonlinear dynamics
• Forecasting Turbulent Modes with Nonparametric Diffusion Models: Learning from noisy data
• Mass Exchange Dynamics of Surface and Subsurface Oil in Shallow-Water Transport

Cited by in corpus (4)

• Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism
• Conditional Gaussian Nonlinear System: a Fast Preconditioner and a Cheap Surrogate Model For Complex Nonlinear Systems
• Mass Exchange Dynamics of Surface and Subsurface Oil in Shallow-Water Transport
• Memory-based reduced modelling and data-based estimation of opinion spreading