LAUSR

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.Machine learning: formation energy of crystals from neural network implementationRobust descriptors of the degree of configurational order in a crystal can be formulated using machine learning tools. A team led by Anton Van der Ven at University of California, Santa Barbara, developed an advanced neural network implementation to build accurate lattice model Hamiltonians using a moderate number of correlation functions as descriptors. Using site-centric correlation function descriptors, the formalism can accurately model the formation energies of a synthetic multi-body binary Hamiltonian on face centered cubic crystals, as well as on Li-intercalated TiS2. As a result, complex multi-body interactions may be approximated by non-linear models involving smaller clusters. The approach can be generalized to describe any scalar property of a multi-component crystal, including its formation energy and volume, as a function of the configurational degrees of freedom.