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Utilization of machine learning models and grey wolf optimization method in estimation of pharmaceutical solubility in supercritical CO2
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DOI：10.3389/fchem.2026.1876302.png)
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Abstract
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Accurate prediction of solubility and solvent density in supercritical fluids is essential for the efficient design and optimization of pharmaceutical and chemical processes. In this study; three machine learning regression models—Elastic Net Regression (ENR); Orthogonal Matching Pursuit (OMP); and Gaussian Process Regression (GPR)—were developed to predict the solubility of Crizotinib and the density of supercritical carbon dioxide (ScCO2). The Grey Wolf Optimizer (GWO) algorithm was employed for hyperparameter tuning to enhance model performance and ensure robust generalization. Experimental data covering a temperature range of 308–338 K and a pressure range of 120–270 bar were used for model training and validation. Among the developed models; GPR demonstrated the highest predictive accuracy for both solvent density and solubility. For density prediction; GPR achieved an R2 value of 0.9979; a root mean square error (RMSE) of 4.36; and an average absolute relative deviation (AARD) of 0.35 percent during training. On the test set; the corresponding values were R2 of 0.9847; RMSE of 16.34; and AARD of 2.12 percent. For solubility prediction; the GPR model achieved an R2 of 0.9848; RMSE of 0.0028; and AARD of 4.97 percent on the training set; while test results showed R2 of 0.9831; RMSE of 0.0035; and AARD of 7.70 percent. The ENR and OMP models yielded slightly lower accuracy; confirming the nonlinear nature of the system and the effectiveness of the GPR model in capturing complex thermodynamic relationships. The analysis of model predictions revealed that solvent density increased nearly linearly with pressure and decreased with temperature; while solubility displayed a crossover trend with temperature; reflecting the characteristic behavior of supercritical fluids. Overall; the proposed GWO–GPR hybrid framework provided excellent accuracy; stability; and interpretability; demonstrating its strong potential for modeling complex thermophysical properties and supporting the design of supercritical CO2-based pharmaceutical processes.
Keywords:
solubility
Gaussian process regression
supercritical CO2
Elastic net regression
Orthogonal matching pursuit
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