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