  Dynamics model learning is challenging and at the same time an active field
of research. Due to potential safety critical downstream applications, such as
control tasks, there is a need for theoretical guarantees. While GPs induce
rich theoretical guarantees as function approximators in space, they do not
explicitly cope with the time aspect of dynamical systems. However, propagating
system properties through time is exactly what classical numerical integrators
were designed for. We introduce a recurrent sparse Gaussian process based
variational inference scheme that is able to discretize the underlying system
with any explicit or implicit single or multistep integrator, thus leveraging
properties of numerical integrators. In particular we discuss Hamiltonian
problems coupled with symplectic integrators producing volume preserving
predictions.
