Second-order AAA algorithms for structured data-driven modeling

[2506.02241] Second-order AAA algorithms for structured data-driven modeling Skip to main content Search Submit Donate Log in Mathematics > Numerical Analysis arXiv:2506.02241 (math) [Submitted on 2 Jun 2025] Title: Second-order AAA algorithms for structured data-driven modeling Authors: Michael S. Ackermann , Ion Victor Gosea , Serkan Gugercin , Steffen W. R. Werner View PDF HTML (experimental) Abstract: The data-driven modeling of dynamical systems has become an essential tool for the construction of accurate computational models from real-world data. In this process, the inherent differential structures underlying the considered physical phenomena are often neglected making the reinterpretation of the learned models in a physically meaningful sense very challenging. In this work, we present three data-driven modeling approaches for the construction of dynamical systems with second-order differential structure directly from frequency domain data. Based on the second-order structured barycentric form, we extend the well-known Adaptive Antoulas-Anderson algorithm to the case of second-order systems. Depending on the available computational resources, we propose variations of the proposed method that prioritize either higher computation speed or greater modeling accuracy, and we present a theoretical analysis for the expected accuracy and performance of the proposed methods. Three numerical examples demonstrate the effectiveness of our new structured approaches in comparison to classical unstructured data-driven modeling. Comments: 37 pages, 6 figures, 3 tables Subjects: Numerical Analysis (math.NA) ; Machine Learning (cs.LG); Systems and Control (eess.SY); Dynamical Systems (math.DS); Optimization and Control (math.OC) MSC classes: 41A20, 65D15, 93B15, 93C05, 93C80 Cite as: arXiv:2506.02241 [math.NA] (or arXiv:2506.02241v1 [math.NA] for this version) https://doi.org/10.48550/arXiv.2506.02241 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Adv. Comput. Math., 52(5):76, 2026 Related DOI : https://doi.org/10.1007/s10444-026-10347-y Focus to learn more DOI(s) linking to related resources Submission history From: Steffen W. R. Werner [ view email ] [v1] Mon, 2 Jun 2025 20:34:18 UTC (1,170 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2025-06 Change to browse by: cs cs.LG cs.NA cs.SY eess eess.SY math math.DS math.OC References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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