A novel compute intensification methodology to the construction of low-dimensional, high-fidelity "compact" kinetic models for NOX formation is designed and demonstrated. The method adapts the data intensive Machine Learned Optimization of Chemical Kinetics (MLOCK) algorithm for compact model generation by the use of a Latin Square method for virtual reaction network generation. A set of logical rules are defined which construct a minimally sized virtual reaction network comprising three additional nodes (N, NO, NO2). This NOX virtual reaction network is appended to a pre-existing compact model for methane combustion comprising fifteen nodes. The resulting eighteen node virtual reaction network is processed by the MLOCK coded algorithm to produce a plethora of compact model candidates for NOX formation during methane combustion. MLOCK automatically; populates the terms of the virtual reaction network with candidate inputs; measures the success of the resulting compact model candidates (in reproducing a broad set of gas turbine industry-defined performance targets); selects regions of input parameters space showing models of best performance; refines the input parameters to give better performance; and makes an ultimate selection of the best performing model or models. By this method, it is shown that a number of compact model candidates exist that show fidelities in excess of 75% in reproducing industry defined performance targets, with one model valid to >75% across fuel/air equivalence ratios of 0.5-1.0. However, to meet the full fuel/air equivalence ratio performance envelope defined by industry, we show that with this minimal virtual reaction network, two further compact models are required.