Seminar| Institute of Mathematical Sciences
Time: Thursday, August 15th, 2024 , 14:00-15:00
Speaker: Zhen Gao, Ocean University of China
Abstrct: Accurately constructing a reduced order model (ROM) of parameterized partial differential equations (PDEs) has always been the challenging problem in engineering and applied sciences. Dynamic mode decomposition (DMD) is a popular and efficient data-driven method for ROM, however, it is proposed for the model order reduction of time-dependent problems that it is invalid for the parameterized problems. In this talk, a new ROM is proposed based on k-nearest neighborhood (KNN) and DMD, namely, KNN-DMD. The KNN can be used to approximate the solution at any given parameter by choosing and averaging the nearest k DMD solutions based on the distance between the given parameter and other parameters. We apply the proposed method to various parameterized PDEs. The results demonstrate the applicability and efficiency of the proposed KNN-DMD as a real-time ROM for parameterized PDEs. Furthermore, KNN-DMD shows better predictive ability than the POD-based ROMs at the outside of the training time region.