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We develop novel surrogate modeling strategies that allow state-of-the-art rational approximation algorithms (e.g., AAA and vector fitting) to better handle data coming from such systems with non-trivial relative degree. Our contribution is twofold. On one hand, we describe a strategy to build rational surrogate models with\n                    <jats:italic>prescribed relative degree<\/jats:italic>\n                    , with the objective of mirroring the high-frequency behavior of the high-fidelity problem, when known. The surrogate model\u2019s desired degree is achieved through constraints on its barycentric coefficients, rather than through ad-hoc modifications of the rational form. On the other hand, we present a degree-identification routine that allows one to estimate the\n                    <jats:italic>unknown relative degree<\/jats:italic>\n                    of a system from low-frequency data. By identifying the degree of the system that generated the data, we can build a surrogate model that, in addition to matching the data well (at low frequencies), has enhanced extrapolation capabilities (at high frequencies). We showcase the effectiveness and robustness of the newly proposed method through a suite of numerical tests.\n                  <\/jats:p>","DOI":"10.1007\/s10915-026-03215-w","type":"journal-article","created":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T06:44:34Z","timestamp":1772001874000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Barycentric Rational Approximation for Learning the Index of a Dynamical System from Limited Data"],"prefix":"10.1007","volume":"107","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0398-1580","authenticated-orcid":false,"given":"Davide","family":"Pradovera","sequence":"first","affiliation":[]},{"given":"Ion Victor","family":"Gosea","sequence":"additional","affiliation":[]},{"given":"Jan","family":"Heiland","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,2,25]]},"reference":[{"issue":"1","key":"3215_CR1","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/s11044-016-9558-z","volume":"40","author":"R Altmann","year":"2017","unstructured":"Altmann, R., Heiland, J.: Simulation of multibody systems with servo constraints through optimal control. 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