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.

中文翻译：

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通过动态模式分解增强多项式混沌以降低动态模型的阶数

由于计算成本低，降阶模型 (ROM) 在基于集成的模拟中是不可或缺的，例如用于不确定性量化、逆向建模和优化。由于用于训练 ROM 的数据通常是通过多次运行高保真模型 (HFM) 获得的，因此 ROM 的效率取决于与数据生成和训练阶段相关的计算成本。其中一种 ROM，即多项式混沌展开 (PCE)，通常提供模型参数空间中 HFM 响应面的稳健描述。为了降低数据生成成本，我们建议在多保真数据上训练PCE，其中一部分来自动态HFM，其余来自动态模式分解（DMD）；后者用于对 HFM 数据进行及时插值。我们的数值实验证明了所提出方法的准确性，并为插值目的的 DMD 的最佳使用提供了指导。