How to represent crystal structures for machine learning: Towards fast prediction of electronic properties

High-throughput density functional calculations of solids are highly time-consuming. As an alternative, we propose a machine learning approach for the fast prediction of solid-state properties. To achieve this, local spin-density approximation calculations are used as a training set. We focus on predicting the value of the density of electronic states at the Fermi energy. We find that conventional representations of the input data, such as the Coulomb matrix, are not suitable for the training of learning machines in the case of periodic solids. We propose a novel crystal structure representation for which learning and competitive prediction accuracies become possible within an unrestricted class of $spd$ systems of arbitrary unit-cell size.