  Understanding the equation of state of dense QCD matter remains a major
challenge in both nuclear physics and astrophysics. Neutron star observations
from electromagnetic and gravitational wave spectra provide critical insights
into the behavior of dense neutron-rich matter. The next generation of
telescopes and gravitational wave observatories will offer even more detailed
observations of neutron stars. Utilizing deep learning techniques to map
neutron star mass and radius observations to the equation of state allows for
its accurate and reliable determination. This work demonstrates the feasibility
of using deep learning to extract the equation of state directly from neutron
star observational data, and to also obtain related nuclear matter properties
such as the slope, curvature, and skewness of the nuclear symmetry energy at
saturation density. Most importantly, we show that this deep learning approach
is able to reconstruct \textit{realistic} equations of state, and deduce
\textit{realistic} nuclear matter properties. This highlights the potential of
artificial neural networks in providing a reliable and efficient means to
extract crucial information about the equation of state and related properties
of dense neutron-rich matter in the era of multi-messenger astrophysics.
