An effective and performing hysteresis model, based on a deep neural network, with the capability to reproduce the evolution of magnetization processes under arbitrary waveforms of excitation is here presented. The proposed model consists of a standalone multi-layer feed-forward neural network, with reserved input neurons for the past values of both the input (H) and output (M), aiming at the reproduction of the storage mechanism typical of hysteretic systems. The training set has been opportunely prepared starting from a set of simulations, performed by the Preisach hysteresis model. The optimized training procedure, based on multi-stage check of the model performance, will be comprehensively discussed. The comparative analysis between the neural network-based model, implemented at low level of abstraction, and the Preisach model covers additional hysteresis processes, different from those involved in the training. The mild/moderate memory requirement and the significant computational speed make the proposed approach suitable for a future coupling with finite-element analysis.