Machine Learning methods for interatomic potentials: application to boron carbide

Total energies of crystal structures can be calculated to high precision using quantumbased density functional theory (DFT) methods, but the calculations can be time consuming and scale badly with system size. Boron carbide exhibits disorder in the distribution of boron and carbon atoms among the crystallographic sites. A cluster expansion of the DFT energy in a series of pairs, triplets, etc. is prohibitive owing to the structural complexity. We fit the energies using machine learning methods like neural network, Gaussian process and support vector regression based on pair correlations only in order to capture nonlinear effects associated with many-body interactions. We use our interaction model in Monte Carlo simulations to evaluate the phase diagram.