A Splitting Approach to Dynamic Mode Decomposition of Nonlinear Systems

TL;DR

This paper introduces a novel Split DMD optimization framework for applying dynamic mode decomposition to nonlinear PDEs with periodic boundary conditions, aiming to improve computational efficiency while maintaining accuracy.

Contribution

It proposes a new splitting approach to enhance the DMD method's effectiveness for nonlinear PDEs, addressing computational challenges.

Findings

Split DMD reduces computational cost

Maintains accuracy in nonlinear PDE modeling

Improves efficiency of reduced-order models

Abstract

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation time. Optimization techniques are studied to improve either or both of these objectives and decrease the total computational cost of the problem. This paper focuses on the dynamic mode decomposition (DMD) applied to nonlinear PDEs with periodic boundary conditions. It provides a study of a newly proposed optimization framework for the DMD method called the Split DMD.