Learning nonparametric ordinary differential equations from noisy data

Autor:	Lahouel, Kamel, Wells, Michael, Rielly, Victor, Lew, Ethan, Lovitz, David, Jedynak, Bruno M.
Rok vydání:	2022
Předmět:	Statistics - Machine Learning Computer Science - Machine Learning 62G05 65L70 68U99
Druh dokumentu:	Working Paper
Popis:	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. Comment: 25 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.15215 Zobrazit plný text záznamu View this record from Arxiv