Model Reduction via Parametrized Locally Invariant Manifolds: Some Examples

2004/12/08 by Aarti Sawant, Amit Acharya, Sawant, Aarti +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Model Reduction and Neural Networks #Modeling and Simulation Systems #Numerical methods for differential equations #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0412022

37 pages, PDF format

openalex publication_date 2004/12/08 · arxiv created 2005/08/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A method for model reduction in nonlinear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint, the method has the potential of serving as a subgrid modeling tool. From the physical standpoint, it provides a model for interpreting and describing history dependence in coarse-grained response of an autonomous system.

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