There is provided a method for modeling a hydrocarbon reservoir that includes generating a reservoir model that has a plurality of sub regions. A solution surrogate is obtained for a 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. If an approximate solution surrogate does not exist in the database, the sub region is simulated using a training simulation to obtain a set of training parameters comprising state variables and boundary conditions of the sub region. A machine learning algorithm is used to obtain a new solution surrogate based on the set of training parameters. The hydrocarbon reservoir can be simulated using the solution surrogate obtained for the at least one sub region.