Thermodynamic–molecular interdependencies and causal determinants governing pharmaceutical solubility in SC-CO2 systems

Abstract

Accurate prediction of pharmaceutical solubility in supercritical CO₂ (SC-CO₂) systems is critical for green drug formulation and process intensification, yet existing machine learning studies largely prioritize predictive accuracy while overlooking mechanistic interpretability and causal understanding. This study proposes an integrated interpretable artificial intelligence framework for modeling drug solubility in SC-CO₂ by combining high-performance gradient boosting algorithms, explainable machine learning, Bayesian optimization, and causal inference. A curated dataset comprising 1,618 pharmaceutical compounds characterized by molecular weight, melting point, temperature, and pressure was employed. Model interpretability was investigated through SHAP analysis and partial dependence plots to quantify feature contributions and nonlinear response patterns. To move beyond correlation-based interpretation, a domain-constrained causal graph together with input-perturbation (what-if) sensitivity analysis was used to compare predictive importance against hypothesized direct causal contribution, within the limits of an observational, non-experimentally-validated causal structure. Explainability analysis identified pressure, and molecular weight, -specific properties as dominant predictive drivers, while causal analysis revealed melting point as a hidden but structurally influential determinant despite its lower statistical importance. Counterfactual simulations further exposed nonlinear and context-dependent solubility responses under ± 20% perturbations of key variables, highlighting asymmetric system sensitivities. Additionally, interaction analysis uncovered strong thermodynamic coupling effects, particularly between pressure and temperature, governing solubility dynamics.