A methodology is discussed to automatically determine the parameters of closed budget equations for chemical species mass fractions and energy, in order to simulate spatially filtered flames as required in large eddy simulation (LES). The method accounts for the effects of LES filtering on chemistry and transport by simultaneously optimizing, for a reduced number of species, the Arrhenius reaction rates and a correction to mixture-averaged molecular diffusion coefficients. The objective is to match, for a given filter size, spatially filtered canonical one-dimensional flames simulated with detailed chemistry solutions. This approach is designed for quite well-resolved LES, in which most of the unresolved fluctuations result from flame thickening due to spatial filtering, thus featuring weak levels of sub-grid scale flame wrinkling. Methane-air partially premixed combustion is addressed. A four-step reduced reaction mechanism involving seven species is developed along with mass and heat molecular transport properties. The optimization is performed at atmospheric pressure and at 3 bar, for ranges of fresh gas temperatures [300-650 K] and equivalence ratios [0.4-1.2]. Comparisons with the filtered detailed chemistry solution of a planar propagating front show that the laminar flame speed, the adiabatic flame temperature, the species profiles in the reaction zone, and the flow chemical composition and temperature at equilibrium are adequately predicted. The new sub-grid scale modeling approach is then applied to three-dimensional LES of an industrial gas turbine burner. Good agreement is found between the quantities predicted with LES and experimental data, in terms of flow and flame dynamics, axial velocities, averaged temperatures, and some major species concentrations. Results are also improved compared to previous simulations of the same burner.