  We introduce a dynamical spatio-temporal model formalized as a recurrent
neural network for forecasting time series of spatial processes, i.e. series of
observations sharing temporal and spatial dependencies. The model learns these
dependencies through a structured latent dynamical component, while a decoder
predicts the observations from the latent representations. We consider several
variants of this model, corresponding to different prior hypothesis about the
spatial relations between the series. The model is evaluated and compared to
state-of-the-art baselines, on a variety of forecasting problems representative
of different application areas: epidemiology, geo-spatial statistics and
car-traffic prediction. Besides these evaluations, we also describe experiments
showing the ability of this approach to extract relevant spatial relations.
