Designing solvent systems is the key to achieving the facile synthesis and separation of desired products from chemical processes. In this regard, many machine-learning models have been developed to predict the solubilities of given solute-solvent pairs. However, breakthroughs in developing predictive models for solubility are needed, which can be accomplished through a remarkable expansion and integration of experimental and computational solubility databases. To maximize predictive accuracy, these two databases should not be separately trained when developing ML models. In addition, they should not be simply combined without reconciling the discrepancies between different magnitudes of errors and uncertainties. Here, we introduce self-evolving solubility databases and graph neural networks developed through semi-supervised self-training approaches. Solubilities from quantum-mechanical calculations are referred to during semi-supervised learning, but they are not directly added to the database. Such methodologies enable the augmentation of databases while correcting the discrepancy between experiments and computation and improving the predictive accuracy against experimental solubilities. The resulting model was successfully applied to two practical examples relevant to solvent selection in organic reactions and separation processes: (i) linear relationship between reaction rates and solvation free energy for three organic reactions, and (ii) partition coefficients for lignin-derived monomers and drug-like molecules.