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.
Identification of linear time-invariant systems with Dynamic Mode Decomposition
Optimal Bounds on Nonlinear Partial Differential Equations in Model Certification, Validation, and Experimental Design
Legendre Expansions of Products of Functions with Applications to Nonlinear Partial Differential Equations
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