Learning nonparametric ordinary differential equations from noisy data
Machine Learning
2023-11-14 v3 Machine Learning
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.
Cite
@article{arxiv.2206.15215,
title = {Learning nonparametric ordinary differential equations from noisy data},
author = {Kamel Lahouel and Michael Wells and Victor Rielly and Ethan Lew and David Lovitz and Bruno M. Jedynak},
journal= {arXiv preprint arXiv:2206.15215},
year = {2023}
}
Comments
25 pages, 6 figures