From CCSD(T) calculations on the water dimer and B97D/CC on the water-circumcoronene complex at a large number of randomly generated conformations, interaction potentials for the physisorption of water on graphene are built, accomplishing almost sub-chemical accuracy. The force fields were constructed by decomposing the interaction in electrostatic and van der Waals contributions, the latter represented through Improved Lennard-Jones potentials. Besides, a CHARMM-like term was included in the water-water potential to improve the description of hydrogen bonds, and an induction term was added to model the polarization effects in the interaction between water and PAH's or graphene. Two schemes with 3 and 6 point-charges were considered for the interactions water-water and water‑PAH, as Coulomb contributions are zero for the water-graphene system. The proposed fitted potentials reproduce the ab initio data used to build them in the whole range of distances and conformations and provide results for selected points very close to CCSD(T) benchmarks. When applied to the water-graphene system, the obtained results are in excellent agreement with p-CCSD(T), revised DFT/SAPPT and DMC reference values. Furthermore, the stability of the various conformers water-PAH and water-graphene, as well as the different trends observed between these systems, is rationalized in terms of the modifications of the electrostatic contribution.