Rapidly converging cluster expansions by transfer learning from empirical potentials*

Cluster expansion (CE) is an effective and widely used method for mapping the potential energy landscape of multicomponent crystalline systems. It enables a systematic and efficient exploration of multidimensional configurational spaces. Despite considerable advances in CE methodologies [1], there remain challenges associated with the sampling of lattice configurations when applied to systems with low symmetry or a high number of chemical components (e.g., high-entropy alloys). In this work, we address these challenges by employing active learning to reduce the number of first-principles calculations in a large training set. Our approach utilizes Bayesian analysis to leverage empirical priors from interatomic potentials, enabling the identification of the most relevant configurations within the training set. To attain this objective, the initial step involves calculating the energy of each structure using empirical potentials, such as COMB3 and EAM, to create a Gaussian distribution. We then enhance this distribution by calculating the energies of most relevant structures using density-functional theory until convergence of the CE enthalpies is achieved. The effectiveness of the approach is tested on the Pt–Ni alloy system, yielding a 2.5-fold decrease in the number of calculations required for constructing a cluster expansion while ensuring robust convergence of the cluster-expanded Hamiltonian with limited statistical fluctuations.

[1] Mueller, Ceder. Phys. Rev. B, 80:024103, 2009.