The extraction of the nuclear matter properties from neutron star
observations is nowadays an important issue, in particular, the properties that
characterize the symmetry energy which are essential to describe correctly
asymmetric nuclear matter. We use deep neural networks (DNN) to map the
relation between cold $\beta $ -equilibrium neutron star matter and the nuclear
matter properties. Assuming a quadratic dependence on the isospin asymmetry for
the energy per particle of homogeneous nuclear matter and using a Taylor
expansion up to fourth order in the iso-scalar and iso-vector contributions, we
generate a dataset of different realizations of $\beta $ -equilibrium NS matter
and the corresponding nuclear matter properties. The DNN model was successfully
trained, attaining great accuracy in the test set. Finally, a real case
scenario was used to test the DNN model, where a set of 33 nuclear models,
obtained within a relativistic mean field approach or a Skyrme force
description, were fed into the DNN model and the corresponding nuclear matter
parameters recovered with considerable accuracy, in particular, the standard
deviations $\sigma ({L}_{\text{sym}})=12.85$ MeV and $\sigma ({K}_{\text{sat}})=41.02$ MeV were obtained, respectively, for the slope of the symmetry energy
and the nuclear matter incompressibility at saturation.