The main goal of the work presented here was to develop, implement and test a highly efficient numerical algorithm for the evaluation of the chemical reaction source terms that appear in the Navier - Stokes equations when a turbulent, premixed, reactive flow is simulated using a finite rate chemistry combustion model. The approach was based on employing Artificial Neural Networks (ANN) that were designed, trained and incorporated into an existing LEM – LES numerical algorithm. Two numerical simulations of reacting flows have been carried out using several techniques for the estimation of the LES filtered reaction rate for the chemical species in laminar and turbulent, premixed, reactive flows, and the results were compared in terms of numerical accuracy and computational speed. It was concluded that the ANN approach provides a significant speedup of the numerical simulation while preserving acceptable accuracy.