  The Equation of State (EoS) of strongly interacting cold and hot ultra-dense
QCD matter remains a major challenge in the field of nuclear astrophysics. With
the advancements in measurements of neutron star masses, radii, and tidal
deformabilities, from electromagnetic and gravitational wave observations,
neutron stars play an important role in constraining the ultra-dense QCD matter
EoS. In this work, we present a novel method that exploits deep learning
techniques to reconstruct the neutron star EoS from mass-radius (M-R)
observations. We employ neural networks (NNs) to represent the EoS in a
model-independent way, within the range of $\sim$1-7 times the nuclear
saturation density. The unsupervised Automatic Differentiation (AD) framework
is implemented to optimize the EoS, so as to yield through TOV equations, an
M-R curve that best fits the observations. We demonstrate that this method
works by rebuilding the EoS on mock data, i.e., mass-radius pairs derived from
a randomly generated polytropic EoS. The reconstructed EoS fits the mock data
with reasonable accuracy, using just 11 mock M-R pairs observations, close to
the current number of actual observations.
