Parametric Dynamic Mode Decomposition for Reduced Order Modeling

TL;DR

This paper introduces two novel parametric Dynamic Mode Decomposition methods that interpolate eigenpairs and operators, enabling efficient reduced-order modeling for parameter-dependent systems, demonstrated on nonlinear diffusion problems.

Contribution

The paper proposes two new parametric DMD techniques based on eigenpair and operator interpolation, improving efficiency over existing stacked approaches.

Findings

The new methods accurately interpolate DMD modes across parameters.

Numerical results show improved computational efficiency.

Methods perform well on nonlinear diffusion and radiative transfer problems.

Abstract

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiples parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. In this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigenpair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.