  Neutron star observables like masses, radii, and tidal deformability are
direct probes to the dense matter equation of state~(EoS). A novel deep
learning method that optimizes an EoS in the automatic differentiation
framework of solving inverse problems is presented. The trained neural network
EoS yields narrow bands for the relationship between the pressure and speed of
sound as a function of the mass density. The results are consistent with those
obtained from conventional approaches and the observational bound on the tidal
deformability inferred from the gravitational wave event, GW170817.
