Second-order AAA algorithms for structured data-driven modeling
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915320272257024 |
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| author | Ackermann, Michael S. Gosea, Ion Victor Gugercin, Serkan Werner, Steffen W. R. |
| author_facet | Ackermann, Michael S. Gosea, Ion Victor Gugercin, Serkan Werner, Steffen W. R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Second-order AAA algorithms for structured data-driven modeling Ackermann, Michael S. Gosea, Ion Victor Gugercin, Serkan Werner, Steffen W. R. Numerical Analysis Machine Learning Systems and Control Dynamical Systems Optimization and Control 41A20, 65D15, 93B15, 93C05, 93C80 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. |
| title | Second-order AAA algorithms for structured data-driven modeling |
| topic | Numerical Analysis Machine Learning Systems and Control Dynamical Systems Optimization and Control 41A20, 65D15, 93B15, 93C05, 93C80 |
| url | https://arxiv.org/abs/2506.02241 |