Machine learning of ab-initio energy landscapes for crystal structure predictions

Abstract

We present a machine learning approach to calculate unrelaxed and relaxed formation energies of compounds relative to the ground state crystal structure of the pure components in the context of structure predictions in binary systems. Typical methods for structure predictions such as genetic algorithms often rely on density-functional theory codes to perform such calculations at a relatively high computational cost. In this work, we explore two commonly used kernel-based learning algorithms, kernel ridge regression and support vector regression. The efficiency of machine learning approaches relies on suitable data representations that encode the relevant physical information about the crystal structures. We select partial radial distribution functions to represent this structural information. We apply the machine learning approaches to the binary Li-Ge system and show that these methods provide small root-mean square prediction errors of about 20 meV/atom across the composition and structure space. Furthermore, we demonstrate that the model can be trained to predict the formation energies of the relaxed structures with the same accuracy when given unrelaxed structures as input. The high accuracy for the prediction of the relaxed energies of unrelaxed structures suggests that the machine-learning method can eliminate unlikely candidate structures from a genetic algorithm search, thus reducing the computational cost required for the explorations of energy landscapes and improving the performance of genetic algorithms for structure predictions.