  Understanding material surfaces and interfaces is vital in applications like
catalysis or electronics. By combining energies from electronic structure with
statistical mechanics, ab initio simulations can in principle predict the
structure of material surfaces as a function of thermodynamic variables.
However, accurate energy simulations are prohibitive when coupled to the vast
phase space that must be statistically sampled. Here, we present a bi-faceted
computational loop to predict surface phase diagrams of multi-component
materials that accelerates both the energy scoring and statistical sampling
methods. Fast, scalable, and data-efficient machine learning interatomic
potentials are trained on high-throughput density-functional theory
calculations through closed-loop active learning. Markov-chain Monte Carlo
sampling in the semi-grand canonical ensemble is enabled by using virtual
surface sites. The predicted surfaces for GaN(0001), Si(111), and SrTiO3(001)
are in agreement with past work and suggest that the proposed strategy can
model complex material surfaces and discover previously unreported surface
terminations.
