Model reduction in stochastic environments

Eric Forgoston, Lora Billings, I. B. Schwartz

Research output: Chapter in Book/Report/Conference proceedingChapter

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.

Original languageEnglish
Title of host publicationInterdisciplinary Mathematical Sciences
PublisherWorld Scientific Publishing Co. Pte. Ltd.
Pages37-61
Number of pages25
DOIs
StatePublished - 1 Jan 2019

Publication series

NameInterdisciplinary Mathematical Sciences
Volume20
ISSN (Print)1793-1355

Fingerprint

Model Reduction
Stochastic Systems
Stochastic systems
Duffing Oscillator
Infectious Diseases
Stochastic Dynamics
Singularly Perturbed
Normal Form
Stochastic Model
Time Scales
High-dimensional
Projection
Stochastic models
Transform
Prediction

Cite this

Forgoston, E., Billings, L., & Schwartz, I. B. (2019). Model reduction in stochastic environments. In Interdisciplinary Mathematical Sciences (pp. 37-61). (Interdisciplinary Mathematical Sciences; Vol. 20). World Scientific Publishing Co. Pte. Ltd.. https://doi.org/10.1142/9789811200359_0003
Forgoston, Eric ; Billings, Lora ; Schwartz, I. B. / Model reduction in stochastic environments. Interdisciplinary Mathematical Sciences. World Scientific Publishing Co. Pte. Ltd., 2019. pp. 37-61 (Interdisciplinary Mathematical Sciences).
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Forgoston, E, Billings, L & Schwartz, IB 2019, Model reduction in stochastic environments. in Interdisciplinary Mathematical Sciences. Interdisciplinary Mathematical Sciences, vol. 20, World Scientific Publishing Co. Pte. Ltd., pp. 37-61. https://doi.org/10.1142/9789811200359_0003

Model reduction in stochastic environments. / Forgoston, Eric; Billings, Lora; Schwartz, I. B.

Interdisciplinary Mathematical Sciences. World Scientific Publishing Co. Pte. Ltd., 2019. p. 37-61 (Interdisciplinary Mathematical Sciences; Vol. 20).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Forgoston E, Billings L, Schwartz IB. Model reduction in stochastic environments. In Interdisciplinary Mathematical Sciences. World Scientific Publishing Co. Pte. Ltd. 2019. p. 37-61. (Interdisciplinary Mathematical Sciences). https://doi.org/10.1142/9789811200359_0003