Data-driven Discovery of Delay Differential Equations with Discrete Delays
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910751090802688 |
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| author | Pecile, Alessandro Demo, Nicola Tezzele, Marco Rozza, Gianluigi Breda, Dimitri |
| author_facet | Pecile, Alessandro Demo, Nicola Tezzele, Marco Rozza, Gianluigi Breda, Dimitri |
| contents | The Sparse Identification of Nonlinear Dynamics (SINDy) framework is a robust method for identifying governing equations, successfully applied to ordinary, partial, and stochastic differential equations. In this work we extend SINDy to identify delay differential equations by using an augmented library that includes delayed samples and Bayesian optimization. To identify a possibly unknown delay we minimize the reconstruction error over a set of candidates. The resulting methodology improves the overall performance by remarkably reducing the number of calls to SINDy with respect to a brute force approach. We also address a multivariate setting to identify multiple unknown delays and (non-multiplicative) parameters. Several numerical tests on delay differential equations with different long-term behavior, number of variables, delays, and parameters support the use of Bayesian optimization highlighting both the efficacy of the proposed methodology and its computational advantages. As a consequence, the class of discoverable models is significantly expanded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven Discovery of Delay Differential Equations with Discrete Delays Pecile, Alessandro Demo, Nicola Tezzele, Marco Rozza, Gianluigi Breda, Dimitri Numerical Analysis Dynamical Systems The Sparse Identification of Nonlinear Dynamics (SINDy) framework is a robust method for identifying governing equations, successfully applied to ordinary, partial, and stochastic differential equations. In this work we extend SINDy to identify delay differential equations by using an augmented library that includes delayed samples and Bayesian optimization. To identify a possibly unknown delay we minimize the reconstruction error over a set of candidates. The resulting methodology improves the overall performance by remarkably reducing the number of calls to SINDy with respect to a brute force approach. We also address a multivariate setting to identify multiple unknown delays and (non-multiplicative) parameters. Several numerical tests on delay differential equations with different long-term behavior, number of variables, delays, and parameters support the use of Bayesian optimization highlighting both the efficacy of the proposed methodology and its computational advantages. As a consequence, the class of discoverable models is significantly expanded. |
| title | Data-driven Discovery of Delay Differential Equations with Discrete Delays |
| topic | Numerical Analysis Dynamical Systems |
| url | https://arxiv.org/abs/2407.19640 |