  Discovery of advanced materials with conventional trial-and-error method
usually suffers tremendous difficulties. Machine learning offers a great
opportunity to discover target materials, but unbalanced distribution of data
often causes less accuracy of the method. Here, we propose the ab initio
Bayesian active learning method that combines the active learning and
high-throughput ab initio calculations to accelerate discovery of desired
functional materials with ultrahigh efficiency and accuracy. We apply it as an
instance to a large family (3,119) of two-dimensional hexagonal binary
compounds with unbalanced data, and accurately screen out the materials with
maximal electric polarizations and proper photovoltaic band gaps, respectively,
whereas the computational costs are significantly reduced by only calculating a
few tenths of possible candidates in comparison to the random search. This
approach shows enormous advantages for the cases with unbalanced distributions
of data. It can be readily applied to seek for a broad range of advanced
materials.
