Model Reduction in Stochastic Environments

TL;DR

This paper introduces a general stochastic model reduction technique using a normal form coordinate transform, enabling accurate lower-dimensional modeling of complex systems with well-separated time scales.

Contribution

It develops a nonlinear stochastic projection method that accurately captures the dynamics of high-dimensional systems in reduced form, applicable to physical and biological models.

Findings

Effective reduction of a singularly perturbed Duffing oscillator

Application to infectious disease outbreak prediction

Maintains dynamics accuracy in reduced models

Abstract

We present a general theory of stochastic model reduction which is based on a normal form coordinate transform method of A.J. Roberts. This nonlinear, stochastic projection allows for the deterministic and stochastic dynamics to interact correctly on the lower-dimensional manifold so that the dynamics predicted by the reduced, stochastic system agrees well with the dynamics predicted by the original, high-dimensional stochastic system. The method may be applied to any system with well-separated time scales. In this article, we consider a physical problem that involves a singularly perturbed Duffing oscillator as well as a biological problem that involves the prediction of infectious disease outbreaks.