Dynamical systems can be modelled by partial differential equations and
numerical computations are used everywhere in science and engineering. In this
work, we investigate the performance of recurrent and convolutional deep neural
network architectures to predict the surface waves. The system is governed by
the Saint-Venant equations. We improve on the long-term prediction over
previous methods while keeping the inference time at a fraction of numerical
simulations. We also show that convolutional networks perform at least as well
as recurrent networks in this task. Finally, we assess the generalisation
capability of each network by extrapolating in longer time-frames and in
different physical settings.