1. A method for modeling a hydrocarbon reservoir, comprising: generating a reservoir model comprising a plurality of sub regions; obtaining a solution surrogate for at least one sub region by: searching a database of existing solution surrogates to obtain an approximate solution surrogate based on a comparison of physical, geometrical, or numerical parameters of the sub region with physical, geometrical, or numerical parameters associated with the existing surrogate solutions in the database; and if an approximate solution surrogate does not exist in the database: simulating the sub region using a training simulation to obtain a set of training parameters comprising state variables and boundary conditions of the sub region; using a machine learning algorithm to obtain a new solution surrogate based on the set of training parameters; and storing the new solution surrogate to the database; simulating the hydrocarbon reservoir using the solution surrogate obtained for the at least one sub region; and generating a data representation of a physical hydrocarbon reservoir in a non-transitory, computer-readable, medium based at least in part on the results of the simulation.