Machine-learning the configurational energy of multicomponent crystalline solids

Machine learning tools such as neural networks and Gaussian process regression are increasingly being implemented in the development of atomistic potentials. Here, we develop a formalism to leverage such non-linear interpolation tools in describing properties dependent on occupation degrees of freedom in multicomponent solids. Symmetry-adapted cluster functions are used to differentiate distinct local orderings. These local features are used as input to neural networks that reproduce local properties such as the site energy. We apply the technique to reproduce a synthetic cluster expansion Hamiltonian with multi-body interactions, as well as the formation energies calculated from first-principles for the intercalation of lithium into TiS2. The formalism and results presented here show that complex multi-body interactions may be approximated by non-linear models involving smaller clusters.