  Astrophysical observations, theoretical models, and terrestrial experiments
probe different regions of neutron star (NS) interior. Therefore, it is
essential to consistently combine the information from these sources. This
analysis requires multiple evaluations of Tolman Oppenheimer Volkoff equations
which can become computationally expensive with a large number of observations.
Further, multi-messenger astronomy requires rapid NS characterization via
gravitational waves for efficient electromagnetic follow-up. In this work, we
develop a novel neural network-based map from the EoS curve to the mass and
radius of cold non-rotating NS. We estimate a speed-up of an order of magnitude
when compared with the state-of-the-art RePrimAnd solver and an average error
of 1e-3 when calculating the mass and radius of the neutron star. Additionally,
we also develop neural network solvers for obtaining EoS curves from a physics
conforming EoS model, FRZ$\chi_{1.5}$. We utilize this efficient continuous map
to measure the sensitivity of model parameters of FRZ$\chi_{1.5}$ towards mass
and radius. We show that 8 out of 18 parameters of this model are sensitive by
at least three orders of magnitude higher than the remaining 10 parameters.
This information will be useful in further speeding up, as well as probing the
crucial parameter space, in the parameter estimation from astrophysical
observations using this physics-conforming EoS model.
