Subsequently we apply a filtering step to the union of generated structures. While the structure generation itself is fast, relaxing these structures using DFT can be a computationally heavy task, so that a filtering process based on structural features to avoid relaxing similar structures is beneficial. This involves calculating the same local atom centered descriptors, Eq. ( ), as we used in the training, but aggregating them over each molecule or structure. Namely, the atomic descriptors are then averaged for each atom type and concatenated, yielding a permutation-invariant descriptor that encapsulates the entire structure: where N A is the number of A atoms. These structural descriptors are then projected onto a lower dimensional space using principal component analysis (PCA) and clustered using k-means clustering. Finally the structures closest to the k-means centroids are chosen as candidate structures. Thus, we use a global descriptor that encompasses the full structure for clustering, while for training and structure generation, we leverage the power of atomic, local descriptors. The selected structures were then relaxed using GPAW with the LDA functional using a 400eV plane wave cutoff. For the periodic structures a 2 × 2 × 2 k-point mesh was used. For the relaxations only these coarse settings were used to reduce the computational cost, since we just required qualitative comparison with the goal structures, but no accurate energies, or even ordering of energy minima. For non-periodic systems, we furthermore confirmed that the same isomers were obtained when using the HF/STO-3G level of theory compared to DFT with the LDA functional (data not shown).