  Active learning is a valuable tool for efficiently exploring complex spaces,
finding a variety of uses in materials science. However, the determination of
convex hulls for phase diagrams does not neatly fit into traditional active
learning approaches due to their global nature. Specifically, the thermodynamic
stability of a material is not simply a function of its own energy, but rather
requires energetic information from all other competing compositions and
phases. Here we present Convex hull-aware Active Learning (CAL), a novel
Bayesian algorithm that chooses experiments to minimize the uncertainty in the
convex hull. CAL prioritizes compositions that are close to or on the hull,
leaving significant uncertainty in other compositions that are quickly
determined to be irrelevant to the convex hull. The convex hull can thus be
predicted with significantly fewer observations than approaches that focus
solely on energy. Intrinsic to this Bayesian approach is uncertainty
quantification in both the convex hull and all subsequent predictions (e.g.,
stability and chemical potential). By providing increased search efficiency and
uncertainty quantification, CAL can be readily incorporated into the emerging
paradigm of uncertainty-based workflows for thermodynamic prediction.
