A generalized and adaptable tensor-contraction-based cluster expansion formalism for multicomponent solids

Density functional theory (DFT)-based simulations of materials have first-principles accuracy, but are very computationally expensive. For simulating various properties of multi-component alloys, the cluster expansion (CE) technique has served as the standard workaround to improve computational efficiency. However, the standard CE technique is difficult to extend to exotic and/or low-symmetry lattices, often implemented via iteration over particular cluster types, which must be enumerated per lattice structure. In this work, we introduce the tensor cluster expansion (TCE), implemented in the open-source code tce-lib, which maps correlation functions to mixed tensor contractions, eliminating the need to iterate over cluster types and additionally making the calculation of correlation functions well-suited for massively parallel architectures like GPUs. We show that local interaction energies are an immediate consequence of the TCE formalism, yielding nearly O ( 1 ) energy difference calculations. We then use this formalism to fit CE models for the TaW and CoNiCrFeMn systems, and use these models to respectively compute the enthalpy of mixing curve and Cowley short-range order parameters, showing excellent agreement with ground truth data. • We introduce a tensor cluster expansion (TCE) effective Hamiltonian for multicomponent solids. • The TCE is generalizable to any periodic lattice, as well as vectorial properties like stress. • Local energies are a direct consequence of the TCE, yielding more efficient Monte Carlo simulations. • Pipelines for training and deploying TCE models are implemented in the open-source code tce-lib. • tce-lib is then used to train and deploy TCE models for TaW and CoNiCrFeMn, in excellent agreement with ground truth data.