Transition Edge Sensors (TES) detector devices, like the one that will be onboard the Athena X-ray Observatory, produce current pulses as a response to the incident X-ray photons. The reconstruction of these pulses aims at recovering the energy of the impacting photon, its arrival time and its physical position in the detector. This has been traditionally performed by means of a triggering algorithm based on the derivative signal overcoming a threshold (detection) followed by optimal filtering (to retrieve the energy of each event). However, when the arrival of the photons is very close in time, the triggering algorithm is incapable of detecting all the individual pulses. Aiming at improving the efficiency of the detection process, we use an alternative approach with Machine Learning techniques. For this purpose, we construct and train a series of Neural Networks (NNs) not only for the detection but also to recover the energy of simulated X-ray pulses. The dataset used to train the NNs consists of simulations performed with SIXTE/xifusim, the Athena/X-IFU official simulator. Although much expensive in terms of computational cost, the performance of our classification NN clearly surpasses the detection performance of the classical triggering approach for the full range of photon energy combinations showing excellent metrics. The reconstruction efficiency for the recovery of the energy of the photons cannot however currently compete with the optimal filtering algorithm.