  Modeling dynamical systems with ordinary differential equations implies a
mechanistic view of the process underlying the dynamics. However in many cases,
this knowledge is not available. To overcome this issue, we introduce a general
framework for nonparametric ODE models using penalized regression in
Reproducing Kernel Hilbert Spaces (RKHS) based on operator-valued kernels.
Moreover, we extend the scope of gradient matching approaches to nonparametric
ODE. A smooth estimate of the solution ODE is built to provide an approximation
of the derivative of the ODE solution which is in turn used to learn the
nonparametric ODE model. This approach benefits from the flexibility of
penalized regression in RKHS allowing for ridge or (structured) sparse
regression as well. Very good results are shown on 3 different ODE systems.
