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

arXiv: https://arxiv.org/abs/2003.06536 · HTML: https://mlsanity.com/paper/2003.06536/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2020.

## Built on by (most cited first, 3 of 3)

- [Rational kernel-based interpolation for complex-valued frequency response functions](https://mlsanity.com/paper/2307.13484/) (2023)
- [Second-order AAA algorithms for structured data-driven modeling](https://mlsanity.com/paper/2506.02241/) (2025)
- [Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison](https://mlsanity.com/paper/2506.12819/) (2025)

## Abstract (arXiv)

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.