A non-transitory machine-readable storage medium is disclosed, which stores a program for modeling a many particle system. When executed on a processing system, the program causes the processing system to (1) determine a compensation function that, when applied to a plurality of interaction equations, compensates for errors introduced by an approximation included in at least one of the plurality of interaction equations, (2) determine an uncompensated solution of the many particle system by solving the many particle system without the plurality of interaction equations, (3) calculate a plurality of observables in the many particle system by solving the many particle system with the plurality of interaction equations by a first iteration, and (4) model the many particle system based on the plurality of observables.