  We investigated the structure of the low density regions of the inner crust
of neutron stars using the Hartree-Fock-Bogoliubov (HFB) model to predict the
proton content $Z$ of the nuclear clusters and, together with the lattice
spacing, the proton content of the crust as a function of the total baryonic
density $\rho_b$. The exploration of the energy surface in the $(Z,\rho_b)$
configuration space and the search for the local minima require thousands of
calculations. Each of them implies an HFB calculation in a box with a large
number of particles, thus making the whole process very demanding. In this
work, we apply a statistical model based on a Gaussian Process Emulator that
makes the exploration of the energy surface ten times faster. We also present a
novel treatment of the HFB equations that leads to an uncertainty on the total
energy of $\approx 4$ keV per particle. Such a high precision is necessary to
distinguish neighbour configurations around the energy minima.
