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

Accurate prediction of drug solubility in supercritical CO₂ remains challenging due to the limited generalizability of compound-specific correlations and the black-box nature of most machine learning models. This study proposes a domain-aware symbolic regression framework that discovers closed-form analytical expressions for ln(y), enabling interpretable and transferable solubility modeling across chemically diverse pharmaceutical compounds. A leave-one-drug-out (LODO) validation strategy is employed to rigorously assess extrapolation performance on unseen drug domains across a curated dataset of 196 experimental data points spanning 9 antihypertensive compounds. Under this evaluation, the domain-adversarial neural network (DANN) component of the proposed framework achieved RMSE = 0.33 ± 0.08, MAE = 0.24 ± 0.06, and R² = 0.89 ± 0.05, outperforming standard machine learning baselines including Random Forest, XGBoost, and Multi-Layer Perceptron in cross-domain generalization. The symbolic regression component additionally recovered compact closed-form analytical expressions that accurately represent the full experimental dataset (in-sample expression fit: R² = 0.962, RMSE = 0.031, MAE = 0.024) while remaining physically interpretable and analytically tractable. The combined framework demonstrates that domain-aware learning and symbolic discovery can jointly address the dual challenge of predictive robustness under domain shift and model interpretability in supercritical pharmaceutical solubility modeling.