  We consider the problem of forecasting complex, nonlinear space-time
processes when observations provide only partial information of on the system's
state. We propose a natural data-driven framework, where the system's dynamics
are modelled by an unknown time-varying differential equation, and the
evolution term is estimated from the data, using a neural network. Any future
state can then be computed by placing the associated differential equation in
an ODE solver. We first evaluate our approach on shallow water and Euler
simulations. We find that our method not only demonstrates high quality
long-term forecasts, but also learns to produce hidden states closely
resembling the true states of the system, without direct supervision on the
latter. Additional experiments conducted on challenging, state of the art ocean
simulations further validate our findings, while exhibiting notable
improvements over classical baselines.
