Symmetric Gradient-Domain Machine Learning (sGDML) is a global kernel ridge regression model designed for efficient force field reconstruction of extended systems. It leverages permutational symmetries to enhance data efficiency and employs a periodic Coulomb descriptor to capture system periodicity accurately. To demonstrate the capabilities of the developed graph-based symmetry search algorithm in combination with global kernel model, we selected four periodic systems in which a 7 × 7 graphene surface interacts with various organic molecules: ethanol, 1,8-naphthyridine, D-alanine, and D-histidine (details provided in the Supplementary Information). For each system, we extracted 400 configurations from DFT-generated molecular dynamics trajectories to identify permutational symmetries and integrate them into the sGDML model in closed form training process. Table presents the mean absolute error (MAE) and root mean squared error (RMSE) values for the sGDML models applied to molecular systems on graphene, along with the number of orbits and permutational symmetries. The results show that the force MAE remains below 1 kcal/(mol•Å) across all systems. While both permutational symmetries and orbits influence the accuracy of sGDML models, the impact of orbits appears to be more significant. Notably, the MAE strongly correlates with the number of orbits, representing atoms in distinct neighborhood chemical compositions. Furthermore, the increasing disparity between RMSE and MAE for forces with a growing number of orbits suggests that atomic force prediction errors are highly heterogeneous, likely due to variations in interaction patterns for different orbits.