Fig. 5: Global optimization of atomic structures in three to six spatial dimensions.

Success curves for global optimization runs without (3D) and with hyperspatial extension (4D, 5D, 6D) of (a) Cu38 cluster, (b) Cu55 cluster, (c) Cu18Ni5 cluster, (d) Ag12S6 cluster, (e) Ta6O15 cluster, (f) Ni15Al5 bulk system. The insets show the identified minimum-energy structures. All success curves include 20 independent runs with 40 surrogate relaxations in each iteration. The error shading is based on Bayesian uncertainty estimation, as detailed in the methods section.