Data-driven H2-optimal Model Reduction via Offline Transfer Function Sampling

TL;DR

This paper introduces an offline sampling method for transfer functions to enable data-driven $ ext{H}_2$-optimal model reduction using IRKA without iterative online measurements, applicable to both continuous and discrete-time systems.

Contribution

It proposes a novel offline transfer function sampling approach that simplifies data-driven $ ext{H}_2$-optimal model reduction, extending IRKA to discrete-time systems using pre-existing data.

Findings

The offline sampling method accurately reproduces transfer functions for model reduction.

The approach reduces the need for iterative measurements during IRKA updates.

Numerical results confirm the effectiveness of the offline sampling in discrete-time systems.

Abstract

$\mathcal{H}_2$-optimal model order reduction algorithms represent a significant class of techniques, known for their accuracy, which has been extensively validated over the past two decades. Among these, the Iterative Rational Krylov Algorithm (IRKA) is widely regarded as a benchmark for constructing $\mathcal{H}_2$-optimal reduced-order models. However, a key challenge in its data-driven implementation lies in the need for transfer function samples and their derivatives, which must be updated iteratively. Conducting new experiments to acquire these samples each time IRKA updates the interpolation data is impractical. Additionally, for discrete-time systems, obtaining transfer function samples at frequencies outside the unit circle is challenging, as these are not easily accessible through measurements. This paper proposes a method to sample the transfer function and its derivative offline using frequency or time-domain data, which is commonly measured for various design and analysis purposes in industry. By leveraging this approach, there is no need to directly measure transfer function samples at interpolation points, as these can be generated offline using the pre-existing data. This facilitates the offline implementation of IRKA within the frequency- or time-domain Loewner framework. The approach is also extended to discrete-time systems in this work. A numerical example is provided to validate the theoretical findings presented.