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

A Splitting Approach to Dynamic Mode Decomposition of Nonlinear Systems