The p-AAA algorithm for data driven modeling of parametric dynamical systems

TL;DR

This paper extends the AAA algorithm to multivariate and matrix-valued functions for data-driven modeling of parametric dynamical systems, enabling efficient approximation from function evaluations without full model access.

Contribution

The paper introduces a multivariate barycentric AAA framework for parametric systems, including matrix-valued functions, connecting it to tangential interpolation theory.

Findings

Effective approximation demonstrated through numerical examples

Extension to matrix-valued functions for multi-input/multi-output systems

No need for full state-space models, only function evaluations

Abstract

The AAA algorithm has become a popular tool for data-driven rational approximation of single variable functions, such as transfer functions of a linear dynamical system. In the setting of parametric dynamical systems appearing in many prominent applications, the underlying (transfer) function to be modeled is a multivariate function. With this in mind, we develop the AAA framework for approximating multivariate functions where the approximant is constructed in the multivariate barycentric form. The method is data-driven, in the sense that it does not require access to full state-space model and requires only function evaluations. We discuss an extension to the case of matrix-valued functions, i.e., multi-input/multi-output dynamical systems, and provide a connection to the tangential interpolation theory. Several numerical examples illustrate the effectiveness of the proposed approach.