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Sci. Comput."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>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 the 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. 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