To use these edge descriptors dij in models, we expand them with a Gaussian smearing function and concatenate with distances εij expanded with radial basis function specific to networks. Also, we present a simple and versatile representation of catalytically active sites, applicable to any GNN-based models for surfaces. Our approach involves labelling the binding site atoms of the unrelaxed bare surface geometry. From the initial structure, a subgraph was generated with binary labelling of catalyst atoms, where all atoms satisfying the following condition were labelled as 1: