Solubility of Glibenclamide in supercritical solvent versus pressure and temperature via development of machine learning and rain optimization algorithm

This study develops machine-learning models for predicting the solubility of Glibenclamide and the density of supercritical CO₂ under varying temperature and pressure conditions. Three regression techniques—Polynomial Kernel Ridge Regression (PKR), Weighted Least Squares (WLS), and Gradient Boosting Trees (GBT)—were employed, with hyperparameters optimized via the Rain Optimization Algorithm (ROA). PKR delivered the highest solubility-prediction accuracy, achieving an R 2 of 0.98689, RMSE of 3.1884 × 10⁻ 1 , MAE of 2.73613 × 10⁻ 1 , and MAPE of 1.33900 × 10⁰. For density prediction, PKR also performed best, with an R 2 of 0.98169, RMSE of 2.0935 × 10 1 , MAE of 1.70231 × 10 1 , and MAPE of 2.92063 × 10⁻ 2 . GBT showed competitive performance (R 2 = 0.93256 for solubility; 0.91889 for density), while WLS produced moderate accuracy. In comparison with previous studies that modeled Glibenclamide solubility using simpler machine-learning methods, the present work introduces an advanced PKR–ROA framework capable of accurately predicting both solubility and supercritical-fluid density. The proposed approach provides a practical computational tool for optimizing SC-CO₂-based pharmaceutical processing.