Parametric Dynamic Mode Decomposition for Reduced Order Modeling

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.

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

“…The parametric DMD method in this section is similar to the partitioned approach in [1], except that we use the autoencoder to generate the latent space rather than the classic POD. There are also other parametric DMD approaches, such as interpolating the DMD eigenpairs or operators [19], using manifold interpolation [15]. In a very recent work [9], the autoencoder is combined with the SINDy approach for periodic problems.…”