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

Neural network reconstruction of the dense matter equation of state from neutron star observables