A kernel-based approach to physics-informed nonlinear system identification
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909851683127296 |
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| author | Donati, Cesare Mammarella, Martina Calafiore, Giuseppe C. Dabbene, Fabrizio Lagoa, Constantino Novara, Carlo |
| author_facet | Donati, Cesare Mammarella, Martina Calafiore, Giuseppe C. Dabbene, Fabrizio Lagoa, Constantino Novara, Carlo |
| contents | This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly embed partially known physics-based models, improving parameter estimation and overall model accuracy. The proposed method enhances traditional modeling approaches by embedding a parametric model, which provides physical interpretability, with a kernel-based function, which accounts for unmodeled dynamics. The two models' components are identified from the data simultaneously, thereby minimizing a suitable cost that balances the relative importance of the physical and the black-box parts of the model. Additionally, nonlinear state smoothing is employed to address scenarios involving state-space models with not fully measurable states. Numerical simulations on an experimental benchmark system demonstrate the effectiveness of the proposed approach, achieving up to 51% reduction in simulation root mean square error compared to physics-only models and 31% performance improvement over state-of-the-art identification techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07634 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A kernel-based approach to physics-informed nonlinear system identification Donati, Cesare Mammarella, Martina Calafiore, Giuseppe C. Dabbene, Fabrizio Lagoa, Constantino Novara, Carlo Systems and Control This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly embed partially known physics-based models, improving parameter estimation and overall model accuracy. The proposed method enhances traditional modeling approaches by embedding a parametric model, which provides physical interpretability, with a kernel-based function, which accounts for unmodeled dynamics. The two models' components are identified from the data simultaneously, thereby minimizing a suitable cost that balances the relative importance of the physical and the black-box parts of the model. Additionally, nonlinear state smoothing is employed to address scenarios involving state-space models with not fully measurable states. Numerical simulations on an experimental benchmark system demonstrate the effectiveness of the proposed approach, achieving up to 51% reduction in simulation root mean square error compared to physics-only models and 31% performance improvement over state-of-the-art identification techniques. |
| title | A kernel-based approach to physics-informed nonlinear system identification |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2509.07634 |