Time-Domain Iterative Rational Krylov Method

This is the authors' abstract. We don't add key points for this paper.

The Realization Independent Iterative Rational Krylov Algorithm (TF-IRKA) is a frequency-based data-driven reduced order modeling (DDROM) method that constructs [Formula: see text] optimal DDROMs. However, as the [Formula: see text] optimal approximation theory dictates, TF-IRKA requires repeated sampling of frequency data, that is, values of the system transfer function and its derivative, outside the unit circle. This repeated evaluation of frequency data requires repeated full model computations and may not be feasible. The data informativity framework for moment matching provides a method for obtaining such frequency data from a single time-domain simulation. However, this framework usually requires solving linear systems with prohibitively ill-conditioned matrices, especially when recovering frequency data from off the unit circle as required for optimality. In this paper, building upon our previous work with the data-informativity framework for moment matching, we provide a formula for the nonzero extreme eigenvalues of a symmetric rank-1 perturbation to an orthogonal projection, which then leads to an optimal scaling of the aforementioned linear systems. We also establish connections between the underlying dynamical system and conditioning of these linear systems. This analysis then leads to our algorithmic development, time-domain IRKA, which allows us to implement a time-domain variant of TF-IRKA, constructing [Formula: see text] optimal DDROMs from a single time-domain simulation without requiring repeated frequency data evaluations. The numerical examples illustrate the effectiveness of the proposed algorithm. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://zenodo.org/records/12751391 . [Formula: see text]