Staged Training of Machine-Learning Potentials from Small to Large Surface Unit Cells: Efficient Global Structure Determination of the RuO₂(100)-c(2 × 2) Reconstruction and (410) Vicinal

Machine-learning (ML) potentials trained with density functional theory (DFT) data boost the sampling capabilities in first-principles global surface structure determination. Particular data efficiency is thereby achieved by iterative training protocols that blend the creation of new training data with the actual surface exploration process. Here, we extend this to a staged training from small to large surface unit cells. With many geometric motifs learned from small unit cell data, successively less new DFT structures in computationally demanding large surface unit cells are queried. We demonstrate the fully automatized workflow in the context of rutile RuO₂ surfaces. For a Gaussian approximation potential (GAP) initially trained on (1 × 1) surface structures, only limited additional data are necessary to efficiently recover only recently identified structures for the RuO₂(100)-c(2 × 2) reconstruction. The same holds when retraining this GAP for the (410) vicinal, the optimized structure of which is found to involve c(2 × 2) reconstructed terraces. Due to the high stability of this structure, (410) vicinals appear in the predicted Wulff equilibrium nanoparticle shape.