Prediction of the flame shape, its stabilization process, and the production of pollutants in practical burners requires the use of detailed chemistry. But detailed schemes introduce tens of species and require CPU times for numerical simulation of combustion in the burner. One of the chemical kinetics reduction techniques which reduces the CPU time is the flame prolongation of Intrinsic Low Dimensional Manifold (ILDM) (FPI) method. The FPI method involves reducing the number of variables that describe the chemical evolution of the reactive mixture. This is done by the construction of a lookup table with three coordinates - a progress variable c, mixture fraction Z, and enthalpy h-and by solving only three transport equations for these variables. All other species are then extracted from the lookup table. In the present study, after a short description of the FPI method, we focus on its validation in the case of premixed diluted methane/air flames. First a validation case is presented to check the capability of the FPI method to reproduce the behavior of a complex chemistry combustion under adiabatic assumption. We study the flame structure in a counterflow flow of a premixed methane/air mixture against fresh air. After this validation, a comparison between detailed chemistry and FPI calculations is presented for the case of a two-dimensional partially premixed nonadiabatic laminar burner. This implies the use of an FPI lookup table with three variables (c, Z, h). It is shown that the FPI model can reproduce the structure of premixed diluted flames, which generally require chemical kinetics including tens of chemical species.