A reduced order method for nonlinear parameterized partial differential equations using dynamic mode decomposition coupled with k-nearest-neighbors regression

Abstract

Accurately constructing a reduced order model (ROM) of nonlinear parameterized partial differential equations (PDEs) has always been a 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 inapplicable for the parameterized problems. In this paper, a new ROM is …