Large eddy simulation of a flameless combustion furnace is discussed with comparison against experimental measurements of the mean thermochemical quantities. The focus is on the introduction in flow simulations of complex chemistry through the training of neural networks, in order to simulate the oxidation of a gaseous fuel representative of recycled gases available in the steel industry. A canonical problem, based on a non-adiabatic stochastic micro-mixing model and combined with a detailed description of chemistry, is setup to train the neural networks prior to the flow simulation. For these networks to be predictive, the thermochemical composition space is decomposed into sub-domains from a partitioning algorithm. A neural network is trained in every sub-domain to return the increments in time of the most influential thermochemical quantities, from the knowledge of temperature and species mass fractions solved with the flow. Implemented in an open-source low-Mach number fluid mechanics code, the neural networks complex chemistry is shown to be very efficient in terms of CPU time, with an overhead of only 60% compared to the non-reactive multi-species simulation of the furnace.