  We aim to identify the generating, ordinary differential equation (ODE) from
a set of trajectories of a partially observed system. Our approach does not
need prescribed basis functions to learn the ODE model, but only a rich set of
Neural Arithmetic Units. For maximal explainability of the learnt model, we
minimise the state size of the ODE as well as the number of non-zero parameters
that are needed to solve the problem. This sparsification is realized through a
combination of the Variational Auto-Encoder (VAE) and Automatic Relevance
Determination (ARD). We show that it is possible to learn not only one specific
model for a single process, but a manifold of models representing harmonic
signals as well as a manifold of Lotka-Volterra systems.
