  Gravitational-wave observations of binary neutron-star (BNS) mergers have the
potential to revolutionize our understanding of the nuclear equation of state
(EOS) and the fundamental interactions that determine its properties. However,
Bayesian parameter estimation frameworks do not typically sample over
microscopic nuclear-physics parameters that determine the EOS. One of the major
hurdles in doing so is the computational cost involved in solving the
neutron-star structure equations, known as the Tolman-Oppenheimer-Volkoff (TOV)
equations. In this paper, we explore approaches to emulating solutions for the
TOV equations: Multilayer Perceptrons (MLP), Gaussian Processes (GP), and a
data-driven variant of the reduced basis method (RBM). We implement these
emulators for three different parameterizations of the nuclear EOS, each with a
different degree of complexity represented by the number of model parameters.
We find that our MLP-based emulators are generally more accurate than the other
two algorithms whereas the RBM results in the largest speedup with respect to
the full, high-fidelity TOV solver. We employ these emulators for a simple
parameter inference using a potentially loud BNS observation, and show that the
posteriors predicted by our emulators are in excellent agreement with those
obtained from the full TOV solver.
