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 R² 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 R² of 0.98169, RMSE of 2.0935 × 10¹, MAE of 1.70231 × 10¹, and MAPE of 2.92063 × 10⁻². GBT showed competitive performance (R² = 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.