Adaptive Simulation Selection for the Discovery of the Ground State Line of Binary Alloys with a Limited Computational Budget

First principles calculations are computationally expensive. This information acquisition cost, combined with an exponentially high number of possible material configurations, constitutes an important roadblock towards the ultimate goal of materials by design. To overcome this barrier, one must devise schemes for the automatic and maximally informative selection of simulations. Such information acquisition decisions are task-dependent, in the sense that an optimal information acquisition policy for learning about a specific material property will not necessarily be optimal for learning about another. In this work, we develop an information acquisition policy for learning the ground state line (GSL) of binary alloys. Our approach is based on a Bayesian interpretation of the cluster expanded energy. This probabilistic surrogate of the energy enables us to quantify the epistemic uncertainty induced by the limited number of simulations which, in turn, is the key to defining a function of the configuration space that quantifies the expected improvement to the GSL resulting from a hypothetical simulation. We show that optimal information acquisition policies should balance the maximization of the expected improvement of the GSL and the minimization of the size of the simulated structure. We validate our approach by learning the GSLs of NiAl and TiAl binary alloys, where to establish the ground truth GSL we use the embedded-atom method (EAM) for the calculation of the energy of a given alloy configuration. Note that the proposed policies are directly applicable to the discovery of generic phase diagrams, if one can construct a probabilistic surrogate of the relevant thermodynamic potential.