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.

Memory-Based Reduced Modelling and Data-Based Estimation of Opinion Spreading

“…If it is reasonable to assume a sufficiently fast decay of the terms h k with increasing k, the memory terms that lie far in the past have negligible influence (Horenko et al 2007;Venkataramani et al 2017;Chorin et al 2000;Zhu et al 2018). In light of (2.5) and (2.6), it is sufficient that the ρ k decay fast.…”