Symbolic and domain-generalized machine learning for interpretable solubility modeling in supercritical CO₂

Area of Science:

• Chemical Engineering
• Computational Chemistry
• Pharmaceutical Sciences

Background:

• Predicting drug solubility in supercritical CO₂ is crucial for pharmaceutical development but hindered by model limitations.
• Existing methods struggle with generalizability and interpretability, especially across different chemical compounds.

Purpose of the Study:

• To develop a domain-aware symbolic regression framework for accurate and interpretable modeling of drug solubility in supercritical CO₂.
• To enable transferable solubility predictions across chemically diverse pharmaceutical compounds.

Main Methods:

• A hybrid approach integrating domain-adversarial neural networks (DANN) for domain adaptation and symbolic regression for discovering analytical expressions.
• Utilized a leave-one-drug-out (LODO) validation strategy on a dataset of 196 experimental points for 9 antihypertensive compounds.

Main Results:

• The DANN component demonstrated strong cross-domain generalization with RMSE = 0.33 ± 0.08, MAE = 0.24 ± 0.06, and R² = 0.89 ± 0.05.
• Symbolic regression recovered interpretable, closed-form analytical expressions with high in-sample accuracy (R² = 0.962).
• The framework outperformed standard machine learning models in cross-domain prediction tasks.

Conclusions:

• Domain-aware learning and symbolic discovery effectively address challenges in supercritical solubility modeling.
• The proposed framework enhances predictive robustness under domain shift and provides interpretable models.
• This approach offers a pathway for more reliable and transferable solubility predictions in pharmaceutical research.