  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.
