Bayesian active machine learning for Cluster expansion construction

The Cluster expansion (CE) is a powerful method for representing the energetics of alloys from a fit to first principles energies. However, many common fitting methods are computationally demanding and do not provide the guarantee that the system's ground states are preserved. This paper demonstrates the use of an efficient implementation of a Bayesian algorithm for cluster expansion construction that ensures all the input structural energies are fitted perfectly while reducing computational cost. The method incorporates an active learning scheme that searches for new optimal structures to include in the fit. As performance tests, we calculate the phase diagram of the Fe-Ir system and study the short range order in an equimolar MoNbTaVW system. The new method has been integrated into the Alloy Theoretic Automated Toolkit (ATAT).