Learning nonparametric ordinary differential equations from noisy data

• URL: http://arxiv.org/abs/2206.15215v3
• Date: Mon, 13 Nov 2023 01:52:03 GMT
• Title: Learning nonparametric ordinary differential equations from noisy data
• Authors: Kamel Lahouel, Michael Wells, Victor Rielly, Ethan Lew, David Lovitz, and Bruno M. Jedynak
• Abstract summary: 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 theory of Reproducing Kernel Hilbert Spaces (RKHS) to define candidates for f for which the solution of the ODE exists and is unique. We propose a penalty method that iteratively uses the Representer theorem and Euler approximations to provide a numerical solution.
• Score: 0.10555513406636088
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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