  We have constructed the surface phase diagram of the BaTiO$_{3}$(001) surface
by employing an evolutionary algorithm for surface structure prediction, where
the ferroelectric polarization is included as a degree of freedom. Among over
1000 candidate structures explored, a surface reconstruction of
(2$\times$1)-TiO is discovered to be thermodynamically stable and have the
\emph{p2mm} plane group symmetry as observed experimentally. We find that the
influence of ferroelectric polarization on the surface free energy can be
either negligibly small or sizably large (over 1 eV per ($2 \times 1$)
supercell), depending strongly on the surface structure and resulting in a
significant distinction of surface phase diagram with varying ferroelectric
polarization. It is therefore feasible to control the surface stability by
applying an external electric field. Our results may have important
implications in understanding the surface reconstruction of ferroelectric
materials and tuning surface properties.
