Machine learning enhanced global optimization by clustering local environments to enable bundled atomic energies

We show how to speed up global optimization of molecular structures using machine learning methods. To represent the molecular structures, we introduce the auto-bag feature vector that combines (i) a local feature vector for each atom, (ii) an unsupervised clustering of such feature vectors for many atoms across several structures, and (iii) a count for a given structure of how many times each cluster is represented. During subsequent global optimization searches, accumulated structure-energy relations of relaxed structural candidates are used to assign local energies to each atom using supervised learning. Specifically, the local energies follow from assigning energies to each cluster of local feature vectors and demanding the sum of local energies to amount to the structural energies in the least squares sense. The usefulness of the method is demonstrated in basin hopping searches for 19-atom structures described by single- or double-well Lennard-Jones type potentials and for 24-atom carbon structures described by density functional theory. In all cases, utilizing the local energy information derived on-the-fly enhances the rate at which the global minimum energy structure is found.