The initial process exploration phase of the APE workflow is schematially summarized in Fig. . It starts from any given atomic configuration of the system, and we use our previously described fuzzy classification algorithm DECAF to group all atoms of this configuration into equivalence groups of essentially identical local atomic environments. In brief, DECAF achieves this labeling by first converting the local environment around each atom into a smooth overlap of atomic positions (SOAP) descriptor . It then embeds this high-dimensional descriptor using multidimensional scaling to perform the categorization with mean shift clustering (MSC) on the resulting low-dimensional embedded vector. Through the use of SOAP, it thus naturally encodes relevant rotation and species permutation symmetries, while the fuzzy classification based on the embedded vector allows atoms with approximately equal atomic environments to still end up in the same equivalence group. What is approximately equal is thereby critically determined by the MSC bandwidth. At large values of this hyperparameter, the fuzzy classification would in the present example merely distinguish terrace, step or corner atoms (essentially resolving their different coordination number). At smaller values, subclasses like different step atoms start to be resolved. Further discussion of DECAF and the alternative choice of using the MACE descriptor instead of SOAP are provided in the SI.