We demonstrate the applicability of the developed approach on examples of a kernel-based model (sGDML) and a message-passing equivariant neural network architecture (MACE). The sGDML model employs a global representation that treats the system as a whole rather than partitioning it into localized atomic contributions. The model ensures permutational invariance by explicitly symmetrizing its predictions through integration over the permutation group of a system. Consequently, incorporating permutational symmetries into the model requires obtaining a comprehensive list of these symmetries. The current implementation uses a spectral graph-matching algorithm limited to non-periodic systems. Our method extends this approach to periodic systems such as those featuring organic molecules interacting with a graphene surface. . In order to achieve this, a number of unique challenges presented by the periodic graph isomorphism problem have to be addressed.