In atomic scale materials modeling (alloy) the cluster expansion (CE) technique is most commonly used for predicting the energy as a function of the distribution of different elements over lattice sites. Such CEs are usually trained to match as closely as possible a series of first-principles calculations and subsequently sampled using Monte Carlo (MC) simulations, which enables one to predict alloy phase diagrams.

More generally, CEs provide a mapping between a configuration and a property of interest. The configuration is not restricted to be atomic but could for example also represent the sequence of amino acids in a protein [NelHarZho13]. Similarly, properties of interest can also be much more general and include for example migration barriers, lattice constants, or transport coefficients [AngLinErh16].

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