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<p>The olive tree (<i>Olea europaea L.</i>) is a rich source of phenolic compounds with recognized bioactivity and broad applications in nutraceutical, pharmaceutical, and food industries. Efficient valorization of these compounds requires accurate prediction of their solubility in supercritical CO<sub>2</sub> (scCO<sub>2</sub>) systems, both in pure solvent and with polar cosolvents. This study evaluates the performance of three semi-empirical correlations (Chrastil, Bartle, and Kumar–Johnston) alongside advanced machine learning (ML) algorithms—Random Forest and XGBoost—for predicting the solubility of key olive-derived phenolics, including oleuropein, hydroxytyrosol, verbascoside, rutin, quercetin, and oleoside. Experimental solubility data were compiled over a wide range of temperature, pressure, and solvent compositions (pure CO<sub>2</sub> and CO<sub>2</sub>–ethanol mixtures up to 30%). Consequently, hydroxytyrosol demonstrated superior solubility, while rutin exhibited the lowest degree of solubility. Ethanol emerged as the most effective cosolvent, substantially enhancing the solubility of the target compounds. Among semi-empirical models, the Bartle equation achieved the best overall accuracy (R<sup>2</sup> ≈ 0.99), while the Chrastil model performed well for single-temperature and crossover predictions. Machine learning models outperformed empirical approaches, with XGBoost and Random Forest achieving R<sup>2</sup> &gt; 0.999 and MAE ≈ 0.02 × 10<sup>–4</sup> mg/g, effectively capturing nonlinear dependencies between operating conditions and solubility. The findings demonstrate the complementarity of mechanistic and data-driven modeling: empirical models provide interpretability and physical insight, whereas machine learning algorithms, including Random Forest and XGBoost, deliver high predictive accuracy along with insights into variable contributions. This integrated approach establishes a robust framework for optimizing supercritical extraction processes and advancing the sustainable valorization of olive-derived phenolics.</p>

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Benchmarking Predictive Models: Empirical vs. ML for Solubility of Olive-Derived Phenolic Compounds in Supercritical Media

  • 期刊论文

  • 发表日期：

    2026年2月4日

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  • Hatem Ksibi

摘要

The olive tree (Olea europaea L.) is a rich source of phenolic compounds with recognized bioactivity and broad applications in nutraceutical, pharmaceutical, and food industries. Efficient valorization of these compounds requires accurate prediction of their solubility in supercritical CO2 (scCO2) systems, both in pure solvent and with polar cosolvents. This study evaluates the performance of three semi-empirical correlations (Chrastil, Bartle, and Kumar–Johnston) alongside advanced machine learning (ML) algorithms—Random Forest and XGBoost—for predicting the solubility of key olive-derived phenolics, including oleuropein, hydroxytyrosol, verbascoside, rutin, quercetin, and oleoside. Experimental solubility data were compiled over a wide range of temperature, pressure, and solvent compositions (pure CO2 and CO2–ethanol mixtures up to 30%). Consequently, hydroxytyrosol demonstrated superior solubility, while rutin exhibited the lowest degree of solubility. Ethanol emerged as the most effective cosolvent, substantially enhancing the solubility of the target compounds. Among semi-empirical models, the Bartle equation achieved the best overall accuracy (R2 ≈ 0.99), while the Chrastil model performed well for single-temperature and crossover predictions. Machine learning models outperformed empirical approaches, with XGBoost and Random Forest achieving R2 > 0.999 and MAE ≈ 0.02 × 10–4 mg/g, effectively capturing nonlinear dependencies between operating conditions and solubility. The findings demonstrate the complementarity of mechanistic and data-driven modeling: empirical models provide interpretability and physical insight, whereas machine learning algorithms, including Random Forest and XGBoost, deliver high predictive accuracy along with insights into variable contributions. This integrated approach establishes a robust framework for optimizing supercritical extraction processes and advancing the sustainable valorization of olive-derived phenolics.