Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929510145851392 |
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| author | Fung, Lloyd Fasel, Urban Juniper, Matthew P. |
| author_facet | Fung, Lloyd Fasel, Urban Juniper, Matthew P. |
| contents | We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy, not only quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data. Using both synthetic and real-life examples such as Lynx-Hare population dynamics, we demonstrate the effectiveness of the new framework in learning correct model equations and compare its computational and data efficiency with existing methods. Because Bayesian-SINDy can quickly assimilate data and is robust against noise, it is particularly suitable for biological data and real-time system identification in control. Its probabilistic framework also enables the calculation of information entropy, laying the foundation for an active learning strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data Fung, Lloyd Fasel, Urban Juniper, Matthew P. Methodology Chaotic Dynamics Machine Learning We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy, not only quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data. Using both synthetic and real-life examples such as Lynx-Hare population dynamics, we demonstrate the effectiveness of the new framework in learning correct model equations and compare its computational and data efficiency with existing methods. Because Bayesian-SINDy can quickly assimilate data and is robust against noise, it is particularly suitable for biological data and real-time system identification in control. Its probabilistic framework also enables the calculation of information entropy, laying the foundation for an active learning strategy. |
| title | Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data |
| topic | Methodology Chaotic Dynamics Machine Learning |
| url | https://arxiv.org/abs/2402.15357 |