\(\boldsymbol{\mathcal{L}_2}\)-使用参数可分形式的最优降阶建模

Petar Mlinaric, S. Gugercin
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引用次数: 0

摘要

我们为线性定常动力系统和平稳参数问题的$\mathcal{L}_2$-最优降阶建模提供了一个统一的框架。利用约简模型量的参数可分形式,我们推导了$\mathcal{L}_2$代价函数相对于约简矩阵的梯度,从而允许非侵入式的、数据驱动的、基于梯度的下降算法仅使用输出样本来构造最优逼近。通过选择适当的度量,框架涵盖了连续(勒贝格)和离散成本函数。通过数值算例验证了该算法的有效性。进一步,我们分析了在什么条件下可以通过投影获得数据驱动的近似。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
\(\boldsymbol{\mathcal{L}_2}\)-Optimal Reduced-Order Modeling Using Parameter-Separable Forms
We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive the gradients of the $\mathcal{L}_2$ cost function with respect to the reduced matrices, which then allows a non-intrusive, data-driven, gradient-based descent algorithm to construct the optimal approximant using only output samples. By choosing an appropriate measure, the framework covers both continuous (Lebesgue) and discrete cost functions. We show the efficacy of the proposed algorithm via various numerical examples. Furthermore, we analyze under what conditions the data-driven approximant can be obtained via projection.
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