High-fidelity prediction of drug solubility in supercritical CO₂ for pharmaceutical applications using advanced computational modeling

Accurately estimating the solubility of drugs in supercritical carbon dioxide (SCCO₂) still represents a major difficulty in drug formulation, separation processes, and green technologies. Traditional empirical and semi-empirical methods usually have a hard time representing the complex non-linear interactions that determine solubility under different thermodynamic conditions (e.g., T and P), which, in turn, restricts their applicability and predictive consistency. This study presents an ensemble framework that combines three machine learning regressors, namely, Extreme Gradient Boosting Regression (XGBR), Light Gradient Boosting Regression (LGBR), and CatBoost Regression (CATr), facilitated by two bio-inspired optimization algorithms, the Artificial Protozoa Optimizer (APO) and the Hippopotamus Optimization Algorithm (HOA) for estimation of pharmaceutical solubility in supercritical CO₂. A dataset of 110 experimental samples reflecting the temperature, pressure, molecular weight (MW), and melting point (MP) of four drugs (Rifampin, Sirolimus, Tacrolimus, and Teriflunomide) was used to model their solubility. Model robustness was ensured through k-fold cross-validation, and interpretability was assessed via SHAP and FAST sensitivity analysis. Additionally, prediction intervals were generated using bootstrapping, enhancing reliability for real-world applications. The ensemble (XGBR + LGBR + CATr optimized by HOA) achieved predictive accuracy (R² = 0.9920, RMSE = 0.08878). The results highlight the potential of optimized ensemble learning in capturing non-linear solubility behaviors, offering a reliable computational framework for pharmaceutical engineering and green drug processing.