  Perovskite oxides have been extensively studied for their wide range of
compositions and structures, as well as their valuable properties for various
applications. Expanding from single perovskite ABO$_3$ to double perovskite
$A_2BB^{\prime}$O$_6$ significantly enhances the ability to tailor specific
physical and chemical properties. However, the vast number of potential
compositions of $A_2BB^{\prime}$O$_6$ makes it impractical to explore them all
experimentally. In this study, we conducted high-throughput calculations to
systematically investigate the structures and stabilities of 4,900
$A_2BB^{\prime}$O$_6$ compositions (with $A$ = Ca, Sr, Ba, and La; $B$ and
$B^{\prime}$ representing metal elements) through over 42,000 density
functional theory (DFT) calculations. Our analysis lead to the discovery of
more than 1,500 new synthesizable $A_2BB^{\prime}$O$_6$ compounds, with over
1,100 of them exhibiting double perovskite structures, predominantly in the
$P2_1/c$ space group. By leveraging the high-throughput dataset, we developed
machine learning models that achieved mean absolute errors of 0.0444 and 0.0330
eV/atom for formation energy and decomposition energy, respectively. Using
these models, we identified 803 stable or metastable compositions beyond the
chemical space covered in our initial calculations, with 612 of them having
DFT-validated decomposition energies below 0.1 eV/atom, resulting in a success
rate of 76.2 \%. This study delineates the stability landscape of
$A_2BB^{\prime}$O$_6$ compounds and offers new insights for the exploration of
these materials.
