Dictionary-based Model Order Reduction via POD-DEIM with Support Vector Machine for the Parametrized Burgers' Equation

In this article, we present a dictionary-based model order reduction approach applied to the parametrized Burgers' equation. This approach uses the support vector machine (SVM) to build a classifier, which efficiently selects the most suitable local reduced-order basis in a dictionary for a given parameter value. The dictionary of local reduced-order models is constructed by clustering the solution manifold enabling the identification of reduced-order bases that are obtained from proper orthogonal decomposition (POD). After a POD basis is chosen by the classifier, it is used in the construction of a reduced-order model corresponding to the parameter value of interest. For the reduced-order modeling task, the Galerkin projection is applied together with the selected POD basis to transform the full-order model to a low-dimensional system. In addition, the discrete empirical interpolation method (DEIM) is applied to further reduce computational complexity of the nonlinear term in Burger's Equation. The numerical experiments for the POD-DEIM reduced-order model assisted by SVM are shown to be efficient in reducing both dimension and simulation time while maintaining accuracy for the parametrized Burgers' equation. Our proposed method is also shown to be more accurate than the standard global basis approach when the same reduced dimension is used.