Nonlinear model order reduction via Dynamic Mode Decomposition

TL;DR

This paper introduces a novel nonlinear model order reduction method using Dynamic Mode Decomposition (DMD), enabling fast, accurate surrogate models for complex dynamical systems without explicitly evaluating nonlinear terms.

Contribution

The paper demonstrates how DMD can be used to efficiently approximate nonlinear terms in reduced order models, improving computational speed while maintaining accuracy.

Findings

Significant computational speed-up achieved.

Accurate approximation of nonlinear dynamics demonstrated.

Effective compared to existing reduction methods.

Abstract

We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the nonlinear term. DMD is a spatio-temporal matrix decomposition of a data matrix that correlates spatial features while simultaneously associating the activity with periodic temporal behavior. With this decomposition, one can obtain a fully reduced dimensional surrogate model and avoid the evaluation of the nonlinear term in the online stage. This allows for an impressive speed up of the computational cost, and, at the same time, accurate approximations of the problem. We present a suite of numerical tests to illustrate our approach and to show the effectiveness of the method in comparison to existing approaches.