A new machine learning methodology is proposed for speeding up thermochemistry computations in simulations of turbulent combustion. The approach is suited to a range of methods including Direct Numerical Simulation (DNS), Probability Density Function (PDF) methods, unsteady flamelet, Conditional Moment Closure (CMC), Multiple Mapping Closure (MMC), Linear Eddy Model (LEM), Thickened Flame Model, the Partially Stirred Reactor (PaSR) method (as in OpenFOAM) and the computation of laminar flames. In these methods, the chemical source term must be evaluated at every time step, and is often the most expensive element of a simulation. The proposed methodology has two main objectives: to offer enhanced capacity for generalisation and to improve the accuracy of the ANN prediction. To accomplish the first objective, we propose a hybrid flamelet/random data (HFRD) method for generating the training set. The random element endows the resulting ANNs with increased capacity for generalisation. Regarding the second objective, a multiple multilayer perceptron (MMP) approach is developed where different multilayer perceptrons (MLPs) are trained to predict states that result in smaller or larger composition changes, as these states feature different dynamics. It is shown that the multiple MLP method can greatly reduce the prediction error, especially for states yielding small composition changes. The approach is used to simulate flamelets of varying strain rates, one-dimensional premixed flames with differential diffusion and varying equivalence ratio, and finally the Large Eddy Simulation (LES) of /air piloted flames Sandia D, E and F, which feature different levels of local extinction. The simulation results show very good agreement with those obtained from direct integration, while the range of problems simulated indicates that the approach has great capacity for generalisation. Finally, a speed-up ratio of 12 is attained for the reaction step.