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240515s2024 xx |||||o 00| ||eng c |
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|a 10.1016/j.jcp.2024.112971
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|a eng
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|a Lahouel, Kamel
|e verfasserin
|4 aut
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| 245 |
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|a Learning nonparametric ordinary differential equations from noisy data
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|c 2024
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|a Text
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|a ƒaComputermedien
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|a ƒa Online-Ressource
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|a Date Revised 17.05.2024
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|a published: Print-Electronic
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|a Citation Status PubMed-not-MEDLINE
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|a Learning nonparametric systems of Ordinary Differential Equations (ODEs) x˙=f(t,x) from noisy data is an emerging machine learning topic. We use the well-developed theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. Learning f consists of solving a constrained optimization problem in an RKHS. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution. We prove a generalization bound for the L2 distance between x and its estimator. Experiments are provided for the FitzHugh-Nagumo oscillator, the Lorenz system, and for predicting the Amyloid level in the cortex of aging subjects. In all cases, we show competitive results compared with the state-of-the-art
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|a Journal Article
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|a Wells, Michael
|e verfasserin
|4 aut
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|a Rielly, Victor
|e verfasserin
|4 aut
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| 700 |
1 |
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|a Lew, Ethan
|e verfasserin
|4 aut
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| 700 |
1 |
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|a Lovitza, David
|e verfasserin
|4 aut
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| 700 |
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|a Jedynak, Bruno M
|e verfasserin
|4 aut
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| 773 |
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|i Enthalten in
|t Journal of computational physics
|d 1986
|g 507(2024) vom: 15. Mai
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|u http://dx.doi.org/10.1016/j.jcp.2024.112971
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