Parametrization of stochastic multiscale triads

TL;DR

This paper explores a model reduction technique for stochastic multiscale systems using linear response theory, comparing it to homogenization and demonstrating its improved accuracy despite higher computational costs.

Contribution

It introduces a weak coupling model reduction method for stochastic systems and discusses its Markovianization, providing a comparison with homogenization for multiscale dynamics.

Findings

Weak coupling method outperforms homogenization in accuracy.

The method results in non-Markovian models that can be Markovianized.

Higher numerical cost but better results in test cases.

Abstract

We discuss applications of a recently developed method for model reduction based on linear response theory of weakly coupled dynamical systems. We apply the weak coupling method to simple stochastic differential equations with slow and fast degrees of freedom. The weak coupling model reduction method results in general in a non-Markovian system, we therefore discuss the Markovianization of the system to allow for straightforward numerical integration. We compare the applied method to the equations obtained through homogenization in the limit of large time scale separation between slow and fast degrees of freedom. We look at ensemble spread from a fixed initial condition, correlation functions and exit times from domain. The weak coupling method gives better results in all test cases, albeit with a higher numerical cost.