Learning nonparametric ordinary differential equations from noisy data.
J Comput Phys
; 5072024 Jun 15.
Article
em En
| MEDLINE
| ID: mdl-38745873
ABSTRACT
Learning nonparametric systems of Ordinary Differential Equations (ODEs) xË=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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MEDLINE
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En
Ano de publicação:
2024
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Article