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G2-OPTIMAL REDUCED-ORDER MODELING USING PARAMETER-SEPARABLE FORMS
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DOI：10.1137/22M1500678.png)
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摘要
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We provide a unifying framework for G2-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 G2 cost function with respect to the reduced matrices, which then allows a nonintrusive, data-driven, gradient-based descent algo-rithm 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.
Keyword:
reduced-order modeling
parametric stationary problems
linear time-invariant sys-tems
optimization
G2 norm
nonlinear least squares
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2.6
论文数:
5.1K
被引数:
1.8W
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