  Oxygen vacancy ordering in perovskite-type transition-metal oxides plays an
important role in the emergence of exotic electronic properties, as typified by
superconducting cuprates. In this study, we predict the stability of
oxygen-deficient perovskite structures in ACuO$_{3-x}$ (A $=$ Ca, Sr, Ba, Sc,
Y, La) by density functional theory calculation. We introduce a combination of
the cluster expansion method, Gaussian process, and Bayesian optimization to
find stable oxygen-deficient structures among a considerable number of
candidates. Our calculations not only reproduce the reported structures but
suggest the presence of several unknown oxygen-deficient perovskite structures,
some of which are stabilized at high pressures. This work demonstrates the
great applicability of the present computational procedure for the elucidation
of the structural stability of strongly correlated oxides with a large
tolerance to oxygen deficiency.
