Learning nonparametric systems of Ordinary Differential Equations (ODEs) 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 for which the solution of the ODE exists and is unique. Learning 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 distance between 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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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11090484 | PMC |
| http://dx.doi.org/10.1016/j.jcp.2024.112971 | DOI Listing |
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