Physics-consistent equation discovery for drug solubility in supercritical CO₂ through symbolic regression and domain...

Predicting drug solubility in supercritical CO₂ is challenging due to limited data, and strong inter-compound variability conditions that hinder generalization to unseen drugs. Although conventional machine learning models often achieve high accuracy, they rely on spurious correlations and lack interpretability, limiting practical use. This study proposes a unified framework combining symbolic regression with domain generalization techniques, including Invariant Risk Minimization (IRM) and Domain-Adversarial Neural Networks (DANN), to enable equation discovery. The framework enables the discovery of invariant, physically consistent equations that generalize beyond the training distribution. Symbolic regression extracts closed-form relationships, while IRM and DANN enforce invariance across domains within a multi-objective optimization setting. The optimized models achieved validation R² values of 0.907, 0.984, and 0.965 for symbolic regression, DANN, and GPR, respectively. Although the highest predictive accuracy was obtained by DANN and GPR, symbolic regression remained competitive under domain-wise evaluation while uniquely providing explicit closed-form relationships between solubility and the governing physicochemical variables. The results therefore demonstrate that predictive performance, interpretability, equation complexity, and physical consistency should be considered jointly when developing transferable models for supercritical CO₂ solubility.