US Patent 9187984 Methods and systems for machine-learning based simulation of flow

There is provided a method for modeling a hydrocarbon reservoir that includes generating a reservoir model that has a plurality of coarse grid cells. A plurality of fine grid models is generated, wherein each fine grid model corresponds to one of the plurality of coarse grid cells that surround a flux interface. The method also includes simulating the plurality of fine grid models using a training simulation to obtain a set of training parameters, including a potential at each coarse grid cell surrounding the flux interface and a flux across the flux interface. A machine learning algorithm is used to generate a constitutive relationship that provides a solution to fluid flow through the flux interface. The method also includes simulating the hydrocarbon reservoir using the constitutive relationship and generating a data representation of a physical hydrocarbon reservoir in a non-transitory, computer-readable medium based on the results of the simulation.