Modeling drug solubility in supercritical CO₂via machine learning

Accurate prediction of pharmaceutical solubility in supercritical carbon dioxide (SC-CO 2 ) can support process design, but small heterogeneous datasets require strict control of target leakage and validation bias. In this study, 196 experimental observations covering different drugs, in the range of 308–343 K, 9–30 MPa, and with CO 2 densities of 326.09–924.56 kg m − 3 were analyzed. The leakage-free input space comprised molecular weight, melting temperature, temperature, pressure, CO2 density, and five pre-specified engineered transformations (rho 1.5 , P 2.8 , TP, T/P, and rho ln rho). A 90/10 development/test split (random seed 5) was used, with hyperparameter selection performed only within the development data; SVR and MLP-ANN scaling was fitted only on training folds. Eight approaches were evaluated including a limited particle-swarm-optimized Random Forest (PSO-RF) approach. On the untouched 20-point test set, Decision Tree produced the highest R 2 (0.955; RMSE 0.217 in Ln(y)) but exactly fitted the development data, whereas PSO-RF, AdaBoost, and Random Forest yielded test R 2 values of 0.920, 0.917, and 0.911, respectively. Repeated nested validation gave mean outer-fold R 2 values of 0.899 ± 0.112 for AdaBoost and 0.908 ± 0.062 for Random Forest. In contrast, leave-one-compound-out validation produced negative pooled R 2 values, demonstrating that interpolation within represented compounds should not be interpreted as reliable prediction for unseen drugs. SHAP analysis was repeated for the leakage-free Random Forest using only the independent test set; molecular weight and melting temperature became the two most influential features, followed by TP and T/P. These findings support the use of the models as interpolation tools within the studied chemical and operating domain, while emphasizing the need for larger chemically diverse external datasets before claims of compound-level generalization can be made.