The determination of the most stable structures of metal clusters supported at solid surfaces by computer simulations represents a formidable challenge due to the complexity of the potential-energy surface. Here, we combine a high-dimensional neural network potential, which allows us to predict the energies and forces of a large number of structures with first-principles accuracy, with a global optimization scheme employing genetic algorithms. This very efficient setup is used to identify the global minima and low-energy local minima for a series of copper clusters containing between four and ten atoms adsorbed at the ZnO(100) surface. A series of structures with common structural features resembling the Cu(111) and Cu(110) surfaces at the metal-oxide interface has been identified, and the geometries of the emerging clusters are characterized in detail. We demonstrate that the frequently employed approximation of a frozen substrate surface in global optimization can result in missing the most relevant structures.
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