Parametric model order reduction by using machine learning techniques

In this dissertation, we present a framework for parametric model order reduction. The proposed methodology called POD-DEIM-GrROM is based on using machine learning technique to build a classifier that automatically selects the best local reduced-order basis in a dictionary for a given parameter value. The dictionary is constructed by clustering the solution manifold enabling the identification of reduced- order bases which are computed from proper orthogonal decomposition (POD). For the reduced-order modeling task, the selected POD basis for the state variable is employed with the Galerkin projection. To further reduce the complexity on nonlinear term, the selected POD basis for system’s nonlinearity is applied with the discrete empirical interpolation method (DEIM). The numerical experiments are performed on 3 parametrized differential equations, which are sine-Gordon equation, Burgers’ equation and the miscible flow in porous media domain. The resulting reduced-order model are demonstrated to be efficient in reducing simulation time while preserving accuracy compared to the global basis approach and Euclidean-based local basis approach. This work also de- rives an error bound for the approximations obtained from the POD-DEIM-GrROM and POD-DEIM-ROM in general setting.