  We present a method for learning generalized Hamiltonian decompositions of
ordinary differential equations given a set of noisy time series measurements.
Our method simultaneously learns a continuous time model and a scalar energy
function for a general dynamical system. Learning predictive models in this
form allows one to place strong, high-level, physics inspired priors onto the
form of the learnt governing equations for general dynamical systems. Moreover,
having shown how our method extends and unifies some previous work in deep
learning with physics inspired priors, we present a novel method for learning
continuous time models from the weak form of the governing equations which is
less computationally taxing than standard adjoint methods.
