A neural mapping is developed to improve the overall performance of Tilecal, which is the hadronic calorimeter of the ATLAS detector. Feeding the input nodes of a multilayer feedforward neural network with the energy values sampled by the calorimeter cells in beam tests, it is shown that the original energy scale of pion beams is reconstructed over a wide energy range and linearity is significantly improved. As it happens for classical methods, a compromise between nonlinearity correction and the optimization of the energy resolution of the detector has to be accomplished. A hybrid training method for the neural mapping is proposed to achieve this design goal. Using the back-propagation algorithm, the method intercalates an epoch of training steps, for which the neural mapping mainly focus on linearity correction, with another block of training steps, in which the original energy resolution obtained by linearly combining the calorimeter cells becomes the main target. ©2001 American Institute of Physics.