Stochastic model reduction for slow-fast systems with moderate time-scale separation

TL;DR

This paper introduces a stochastic model reduction method for slow-fast systems that accounts for finite time-scale separation, improving upon classical homogenization by incorporating Edgeworth expansions for more accurate approximations.

Contribution

It develops a stochastic reduction technique that relaxes the infinite separation assumption, using Edgeworth expansions to match deviations and enhance model accuracy.

Findings

Significant improvement over classical homogenization

Accurate approximation for finite time-scale separation

Validated by numerical examples

Abstract

We propose a stochastic model reduction strategy for deterministic and stochastic slow-fast systems with finite time-scale separation. The stochastic model reduction relaxes the assumption of infinite time-scale separation of classical homogenization theory by incorporating deviations from this limit as described by an Edgeworth expansion. A surrogate system is constructed the parameters of which are matched to produce the same Edgeworth expansions up to any desired order of the original multi-scale system. We corroborate our analytical findings by numerical examples, showing significant improvements to classical homogenized model reduction.