Parametric Dynamic Mode Decomposition for Reduced Order Modeling

Abstract

Dynamic Mode Decomposition (DMD) is a method by which spatial modes can be extracted from experimental or numerical data sets. DMD can be used as well to obtain a low rank or reduced operator for a physical system by singular value decomposition of temporal data sets. This work focuses on an extension of the general DMD algorithm to take advantage of parametric data sets, parametric DMD. Parametric DMD has application in multi-query problems such as design optimization and uncertainty quantification. The work comprises of two novel methods developed reduced eigen-pair interpolation and reduced Koopman operator interpolation and compares these methods to the current state of the art approach for parametric DMD stacked DMD. The methods are compared on a set of problems including a multiphysics radiative transfer example. The reduced Koopman operator interpolation method is shown to have improvement in computational efficiency as well as reconstruction error in select parametric problems.