Polynomial chaos enhanced by dynamic mode decomposition for order-reduction of dynamic models

Abstract

Thanks to their low computational cost, reduced-order models (ROMs) are indispensable in ensemble-based simulations used, e.g., for uncertainty quantification, inverse modeling, and optimization. Since data used to train a ROM are typically obtained by running a high-fidelity model (HFM) multiple times, a ROM’s efficiency rests on the computational cost associated with the data generation and training phase. One such ROM, a polynomial chaos expansion (PCE), often provides a robust description of an HFM’s response surface in the space of model parameters. To reduce the data-generation cost, we propose to train a PCE on multi-fidelity data, part of which come from the dynamic HFM and the remainder from dynamic mode decomposition (DMD); the latter is used to interpolate the HFM data in time. Our numerical experiments demonstrate the accuracy of the proposed method and provide guidelines for the optimal use of DMD for interpolation purposes.