DDE-Find: Learning Delay Differential Equations from Noisy, Limited Data
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916246753116160 |
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| author | Stephany, Robert |
| author_facet | Stephany, Robert |
| contents | Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results can be challenging. We introduce DDE-Find, a data-driven framework for learning a DDE's parameters, time delay, and initial condition function. DDE-Find uses an adjoint-based approach to efficiently compute the gradient of a loss function with respect to the model parameters. We motivate and rigorously prove an expression for the gradients of the loss using the adjoint. DDE-Find builds upon recent developments in learning DDEs from data and delivers the first complete framework for learning DDEs from data. Through a series of numerical experiments, we demonstrate that DDE-Find can learn DDEs from noisy, limited data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | DDE-Find: Learning Delay Differential Equations from Noisy, Limited Data Stephany, Robert Machine Learning Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results can be challenging. We introduce DDE-Find, a data-driven framework for learning a DDE's parameters, time delay, and initial condition function. DDE-Find uses an adjoint-based approach to efficiently compute the gradient of a loss function with respect to the model parameters. We motivate and rigorously prove an expression for the gradients of the loss using the adjoint. DDE-Find builds upon recent developments in learning DDEs from data and delivers the first complete framework for learning DDEs from data. Through a series of numerical experiments, we demonstrate that DDE-Find can learn DDEs from noisy, limited data. |
| title | DDE-Find: Learning Delay Differential Equations from Noisy, Limited Data |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2405.02661 |