  Hamiltonian mechanics is one of the cornerstones of natural sciences.
Recently there has been significant interest in learning Hamiltonian systems in
a free-form way directly from trajectory data. Previous methods have tackled
the problem of learning from many short, low-noise trajectories, but learning
from a small number of long, noisy trajectories, whilst accounting for model
uncertainty has not been addressed. In this work, we present a Gaussian process
model for Hamiltonian systems with efficient decoupled parameterisation, and
introduce an energy-conserving shooting method that allows robust inference
from both short and long trajectories. We demonstrate the method's success in
learning Hamiltonian systems in various data settings.
