G2-OPTIMAL REDUCED-ORDER MODELING USING PARAMETER-SEPARABLE FORMS

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.

Automated summary

We present a unified framework for G2-optimal reduced-order modeling of linear time-invariant dynamical systems and stationary parametric problems. By utilizing parameter-separable forms of the reduced-model quantities, we derive the gradients of the G2 cost function with respect to the reduced matrices, enabling a nonintrusive, data-driven, gradient-based descent algorithm that constructs the optimal approximant solely based on output samples. The framework covers both continuous (Lebesgue) and discrete cost functions by selecting an appropriate measure. Various numerical examples demonstrate the effectiveness of the proposed algorithm. Moreover, we analyze the conditions under which the data-driven approximant can be obtained through projection.