  The ability to simulate the partial differential equations (PDE's) that
govern multi-phase flow in porous media is essential for different applications
such as geologic sequestration of CO2, groundwater flow monitoring and
hydrocarbon recovery from geologic formations [1]. These multi-phase flow
problems can be simulated by solving the governing PDE's numerically, using
various discretization schemes such as finite elements, finite volumes,
spectral methods, etc. More recently, the application of Machine Learning (ML)
to approximate the solutions to PDE's has been a very active research area.
However, most researchers have focused on the performance of their models
within the time-space domain in which the models were trained. In this work, we
apply ML techniques to approximate PDE solutions and focus on the forecasting
problem outside of the training domain. To this end, we use two different ML
architectures - the feed forward neural (FFN) network and the long short-term
memory (LSTM)-based neural network, to predict the PDE solutions in future
times based on the knowledge of the solutions in the past. The results of our
methodology are presented on two example PDE's - namely a form of PDE that
models the underground injection of CO2 and its hyperbolic limit which is a
common benchmark case. In both cases, the LSTM architecture shows a huge
potential to predict the solution behavior at future times based on prior data
