In atomic scale materials modeling the alloy cluster expansion (CE) technique is widely used for predicting the energy as a function of composition. Such CEs are usually trained to match as closely as possible a series of first-principles calculations and subsequently used to sample configuration space with Monte Carlo (MC) simulations. In this way, CEs can be used 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].