Model Reduction in Stochastic Environments

2017/11/20 by Eric Forgoston, Forgoston, Eric, Lora Billings +3
Decision Sciences · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Model Reduction and Neural Networks #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1711.07842

openalex publication_date 2017/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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