A non-intrusive data-based reformulation of a hybrid projection-based model reduction method

TL;DR

This paper introduces a data-driven reformulation of the ISRK model reduction algorithm that relies solely on input/output transfer function data, eliminating the need for original system matrices.

Contribution

It presents a novel non-intrusive approach to the ISRK method, enabling model reduction using only transfer function evaluations rather than system matrices.

Findings

Efficient data-driven reformulation of ISRK

Requires only transfer function data, not system matrices

Numerical examples demonstrate effectiveness

Abstract

We present a novel data-driven reformulation of the iterative SVD-rational Krylov algorithm (ISRK), in its original formulation a Petrov-Galerkin (two-sided) projection-based iterative method for model reduction combining rational Krylov subspaces (on one side) with Gramian/SVD based subspaces (on the other side). We show that in each step of ISRK, we do not necessarily require access to the original system matrices, but only to input/output data in the form of the system's transfer function, evaluated at particular values (frequencies). Numerical examples illustrate the efficiency of the new data-driven formulation.