  The Pierre Auger Observatory, at present the largest cosmic-ray observatory
ever built, is instrumented with a ground array of 1600 water-Cherenkov
detectors, known as the Surface Detector (SD). The SD samples the secondary
particle content (mostly photons, electrons, positrons and muons) of extensive
air showers initiated by cosmic rays with energies ranging from $10^{17}~$eV up
to more than $10^{20}~$eV. Measuring the independent contribution of the muon
component to the total registered signal is crucial to enhance the capability
of the Observatory to estimate the mass of the cosmic rays on an event-by-event
basis. However, with the current design of the SD, it is difficult to
straightforwardly separate the contributions of muons to the SD time traces
from those of photons, electrons and positrons. In this paper, we present a
method aimed at extracting the muon component of the time traces registered
with each individual detector of the SD using Recurrent Neural Networks. We
derive the performances of the method by training the neural network on
simulations, in which the muon and the electromagnetic components of the traces
are known. We conclude this work showing the performance of this method on
experimental data of the Pierre Auger Observatory. We find that our predictions
agree with the parameterizations obtained by the AGASA collaboration to
describe the lateral distributions of the electromagnetic and muonic components
of extensive air showers.
