  Humans gain an implicit understanding of physical laws through observing and
interacting with the world. Endowing an autonomous agent with an understanding
of physical laws through experience and observation is seldom practical: we
should seek alternatives. Fortunately, many of the laws of behaviour of the
physical world can be derived from prior knowledge of dynamical systems,
expressed through the use of partial differential equations. In this work, we
suggest a neural network capable of understanding a specific physical
phenomenon: wave propagation in a two-dimensional medium. We define
`understanding' in this context as the ability to predict the future evolution
of the spatial patterns of rendered wave amplitude from a relatively small set
of initial observations. The inherent complexity of the wave equations --
together with the existence of reflections and interference -- makes the
prediction problem non-trivial. A network capable of making approximate
predictions also unlocks the opportunity to speed-up numerical simulations for
wave propagation. To this aim, we created a novel dataset of simulated wave
motion and built a predictive deep neural network comprising of three main
blocks: an encoder, a propagator made by 3 LSTMs, and a decoder. Results show
reasonable predictions for as long as 80 time steps into the future on a
dataset not seen during training. Furthermore, the network is able to
generalize to an initial condition that is qualitatively different from those
seen during training.
