  Physics perception very often faces the problem that only limited data or
partial measurements on the scene are available. In this work, we propose a
strategy to learn the full state of sloshing liquids from measurements of the
free surface. Our approach is based on recurrent neural networks (RNN) that
project the limited information available to a reduced-order manifold so as to
not only reconstruct the unknown information, but also to be capable of
performing fluid reasoning about future scenarios in real time. To obtain
physically consistent predictions, we train deep neural networks on the
reduced-order manifold that, through the employ of inductive biases, ensure the
fulfillment of the principles of thermodynamics. RNNs learn from history the
required hidden information to correlate the limited information with the
latent space where the simulation occurs. Finally, a decoder returns data back
to the high-dimensional manifold, so as to provide the user with insightful
information in the form of augmented reality. This algorithm is connected to a
computer vision system to test the performance of the proposed methodology with
real information, resulting in a system capable of understanding and predicting
future states of the observed fluid in real-time.
