  We propose a method for the data-driven inference of temporal evolutions of
physical functions with deep learning. More specifically, we target fluid
flows, i.e. Navier-Stokes problems, and we propose a novel LSTM-based approach
to predict the changes of pressure fields over time. The central challenge in
this context is the high dimensionality of Eulerian space-time data sets. We
demonstrate for the first time that dense 3D+time functions of physics system
can be predicted within the latent spaces of neural networks, and we arrive at
a neural-network based simulation algorithm with significant practical
speed-ups. We highlight the capabilities of our method with a series of complex
liquid simulations, and with a set of single-phase buoyancy simulations. With a
set of trained networks, our method is more than two orders of magnitudes
faster than a traditional pressure solver. Additionally, we present and discuss
a series of detailed evaluations for the different components of our algorithm.
