We present a method based on the use of Recurrent Neural Networks to
extract the muon component from the time traces registered with
water-Cherenkov detector (WCD) stations of the Surface Detector of the Pierre
Auger Observatory. The design of the WCDs does not allow to separate the
contribution of muons to the time traces obtained from the WCDs from those of
photons, electrons and positrons for all events. Separating the muon and
electromagnetic components is crucial for the determination of the nature of
the primary cosmic rays and properties of the hadronic interactions at
ultra-high energies.

We trained a neural network to extract the muon and the
electromagnetic components from the WCD traces using a large set
of simulated air showers, with around 450 000 simulated events.
For training and evaluating the performance of the neural network,
simulated events with energies between $10^{18.5},$ eV and $10^{20}$ eV
and zenith angles below 60 degrees were used. We also study the
performance of this method on experimental data of the Pierre
Auger Observatory and show that our predicted muon lateral
distributions agree with the parameterizations obtained by the
AGASA collaboration.