Information about the behavior of molecules in living organisms and the environment can be obtained by preliminary characterization of their biomimetic profile. The biomimetic profile may include the physico-chemical, pharmacokinetic, and ecotoxicological properties of the experimental molecule, determining its practical potential. This approach is widely used in pharmaceutical-oriented disciplines because it directs the further development phase of drugs. In our study, the possibility of applying graph neural networks (GNNs) as a bio-inspired algorithm for predicting Hansen's solubility parameters (HSPs) of molecules was examined. Hansen's solubility parameters consider the characteristics of molecules through the contributions of hydrogen, dispersive, and polar forces. By predicting and understanding these physico-chemical characteristics, the pharmacokinetic profile of the compound and its toxicological potential can be predicted. The best models were selected according to the internal (R²_train, RMSE, MEPcv) and external (RMSEP, CCC, MEP, R²_test, ar²m, Δr²m) validation metrics using a freely available database, https://www.stevenabbott.co.uk. In addition, experimental validation was performed considering the agreement between experimentally obtained HSP data from the literature for 93 compounds and the data predicted by the created models. The results of GNN modeling showed reliable predictive characteristics. For polar and hydrogen bond forces, the coefficient of determination between experimentally obtained and predicted HSP values was greater than 0.76, and for dispersive forces it was greater than 0.66. The created GNN models can be successfully applied in characterizing the biomimetic properties of experimental molecules in preliminary drug profiling.