A computer-implemented method for modeling and simulating a hydrocarbon reservoir, comprising: generating a reservoir model comprising a plurality of coarse grid cells; generating a plurality of fine grid models, each fine grid model corresponding to one of the plurality of coarse grid cells that surround a flux interface in such a way that the boundary between two coarse grid cells is associated with a corresponding flux and is referred to as the flux interface; simulating the plurality of fine grid models using a training simulation to obtain a set of training parameters comprising a potential or a pressure at each coarse grid cell surrounding the flux interface and a flux across the flux interface; using a machine learning algorithm to generate a constitutive relationship that provides a solution to fluid flow through the flux interface; storing the constitutive relationship generated for the flux interface and physical, geometrical, or numerical parameters corresponding to the plurality of coarse grid cells that surround the flux interface to a database of surrogate solutions for use in subsequent reservoir simulations; simulating the hydrocarbon reservoir using the constitutive relationship, wherein the constitutive relationship generated for the flux interface is re-used for a second flux interface based on a comparison of a set of physical, geometrical, or numerical parameters corresponding to the flux interface and a new set of physical, geometrical, or numerical parameters that characterize the second flux interface; 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. generating a reservoir model comprising a plurality of coarse grid cells; generating a plurality of fine grid models, each fine grid model corresponding to one of the plurality of coarse grid cells that surround a flux interface in such a way that the boundary between two coarse grid cells is associated with a corresponding flux and is referred to as the flux interface; simulating the plurality of fine grid models using a training simulation to obtain a set of training parameters comprising a potential or a pressure at each coarse grid cell surrounding the flux interface and a flux across the flux interface; using a machine learning algorithm to generate a constitutive relationship that provides a solution to fluid flow through the flux interface; storing the constitutive relationship generated for the flux interface and physical, geometrical, or numerical parameters corresponding to the plurality of coarse grid cells that surround the flux interface to a database of surrogate solutions for use in subsequent reservoir simulations; simulating the hydrocarbon reservoir using the constitutive relationship, wherein the constitutive relationship generated for the flux interface is re-used for a second flux interface based on a comparison of a set of physical, geometrical, or numerical parameters corresponding to the flux interface and a new set of physical, geometrical, or numerical parameters that characterize the second flux interface; 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. <EOS>