There is provided a method for modeling a hydrocarbon reservoir that includes generating a reservoir model comprising a plurality of sub regions. At least one of the sub regions is simulated using a training simulation to obtain a set of training parameters comprising state variables and boundary conditions of the at least one sub region. A machine learning algorithm is used to approximate, based on the set of training parameters, an inverse operator of a matrix equation that provides a solution to fluid flow through a porous media. The hydrocarbon reservoir can be simulated using the inverse operator approximated for the at least one sub region. The method also includes generating a data representation of a physical hydrocarbon reservoir can be generated in a non-transitory, computer-readable, medium based, at least in part, on the results of the simulation.