Speaker
Description
We introduce a unified approach to $\mathcal{L}_2$-optimal reduced-order modeling that applies to both linear time-invariant dynamical systems and stationary parametric problems. The framework leverages parameter-separable representations to obtain gradient information for the $\mathcal{L}_2$ objective with respect to the reduced operators, enabling a fully nonintrusive, data-driven, gradient-based construction of optimal reduced models from output data alone. By selecting an appropriate measure, the formulation naturally includes both continuous and discrete cost functions. The proposed methodology is validated through representative numerical examples, and conditions guaranteeing a projection-based realization of the data-driven approximant are established.