The APE framework executes close to 45,000 successful dimer searches before this stop criterion is reached. This would impose excessive computational costs, if the associated PES evaluations were directly performed at the first-principles DFT level. We therefore combine the APE exploration with an iterative training of an MLIP, specifically a Gaussian Approximation Potential (GAP), as illustrated in Fig. . An initial GAP training set comprised a total of 520 structures, extending over (optimized and rattled) bulk unit-cells, clean and O-covered Pd(100) and Pd(410) surface structures, as well as the full ( √ 5 × √ 5)R27 • surface oxide, 42 cf. the SI for a full list and description. APE is first run on this GAP PES surrogate model until 500 processes have been obtained. We then perform a farthest point sampling on the average kernel of their smooth overlap of atomic position (SOAP) representation separately for the corresponding local minima (LM) and TS structures using the wfl package. The thus identified 50 maximally diverse LM and TS structures are subject to explicit DFT single-point calculations, and subsequently added to the GAP training set. After retraining, the improved GAP is used to explore the next 500 processes, and this iterative learning loop is continued until the APE stop criterion is reached.