  We present a pipeline to infer the equation of state of neutron stars from
observations based on deep neural networks. In particular, using the standard
(deterministic), as well as Bayesian (probabilistic) deep networks, we explore
how one can infer the interior speed of sound of the star given a set of mock
observations of total stellar mass, stellar radius and tidal deformability. We
discuss in detail the construction of our simulated dataset of stellar
observables starting from the solution of the gravitational equations, as well
as the relevant architectures for the deep networks, along with their
performance and accuracy. We further explain how our pipeline is capable to
detect a possible QCD phase transition in the stellar core. Our results show
that deep networks offer a promising tool towards solving the inverse problem
of neutron stars, and the accurate inference of their interior from future
stellar observations.
