Structured Optimization-Based Model Order Reduction for Parametric Systems

TL;DR

This paper introduces an optimization-based approach for parametric model order reduction of linear systems, achieving high accuracy across parameter domains and enabling structure preservation, outperforming existing methods.

Contribution

It extends the SOBMOR algorithm to parametric systems, optimizing system matrices directly for better accuracy and structure preservation across parameters.

Findings

Achieves lower approximation error across parameter domain.

Enforces structure preservation such as port-Hamiltonian form.

Demonstrates superior performance in numerical examples.

Abstract

We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the frequency and parameter domain by an optimization of the reduced order model (ROM) matrices. State-of-the-art PMOR methods often compute several nonparametric ROMs for different parameter samples, which are then combined to a single parametric ROM. However, these parametric ROMs can have a low accuracy between the utilized sample points. In contrast, our optimization-based PMOR method minimizes the approximation error across the entire parameter domain. Moreover, due to our flexible approach of optimizing the system matrices directly, we can enforce favorable features such as a port-Hamiltonian structure in our ROMs across the entire parameter domain. Our method is an extension of the recently developed SOBMOR-algorithm to parametric systems. We extend both the ROM parameterization and the adaptive sampling procedure to the parametric case. Several numerical examples demonstrate the effectiveness and high accuracy of our method in a comparison with other PMOR methods.