Model Reduction via Parametrized Locally Invariant Manifolds: Some Examples

TL;DR

This paper introduces a new model reduction technique for nonlinear ODE systems using parametrized locally invariant manifolds, effective without explicit time-scale separation, with potential applications in subgrid modeling and understanding history dependence.

Contribution

It presents a novel model reduction method that does not rely on time-scale separation, demonstrated through computational examples, and offers insights into coarse-grained system responses.

Findings

Method effective without explicit time-scale separation

Potential for subgrid modeling applications

Provides interpretation of history dependence in coarse responses

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.