Learning nonparametric ordinary differential equations from noisy data

Kamel Lahouel; Michael Wells; Victor Rielly; Ethan Lew; David Lovitz; Bruno M. Jedynak

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arXiv · 2206.15215

Learning nonparametric ordinary differential equations from noisy data

Kamel Lahouel·Michael Wells·Victor Rielly·Ethan Lew·David Lovitz·Bruno M. Jedynak

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Abstract

Learning nonparametric systems of Ordinary Differential Equations (ODEs) dot 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 and provide experimental comparisons with the state-of-the-art.

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BibTeX RIS

Kamel Lahouel, Michael Wells, Victor Rielly, Ethan Lew, David Lovitz, Bruno M. Jedynak. 2022-06-30. Learning nonparametric ordinary differential equations from noisy data. https://arxiv.org/abs/2206.15215

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