Computational modeling and optimized machine learning for multidrug solubility prediction in supercritical carbon dioxide

Reliable prediction of pharmaceutical solubility in supercritical carbon dioxide (scCO₂) is complicated by strong compound-specific behavior and response values. This study investigated whether sparse measurements from a newly introduced drug can calibrate transferable machine-learning predictions for computational estimation of solubility in wide range of parameters. A curated workbook containing 1,618 observations for 60 drugs was modeled using molecular weight, melting point, temperature, and pressure. Solubility was transformed as log₁₀(S), and XGBoost, CatBoost, and multilayer perceptron regression were each tuned using tree-structured Parzen estimation, differential evolution, and particle swarm optimization. Evaluation used five-fold nested group cross-validation, with complete drugs held out from training and tuning. For each test drug, predictions were assessed before calibration and after 1, 3, or 5 randomly selected measurements, repeated ten times. Within the present evaluation framework, the lowest-log-MAE zero-shot configuration was XGBoost optimized by tree-structured Parzen estimation (log-MAE = 0.584; R² = -0.087; RMSE = 1.713 g/L), showing that the four descriptors were insufficient for reliable extrapolation to unseen compounds. Sparse calibration substantially improved transfer: the lowest-log-MAE one-shot result was obtained by CatBoost-particle swarm optimization (log-MAE = 0.418; R² = 0.166), whereas XGBoost-tree-structured Parzen estimation had the lowest log-MAE at three shots (log-MAE = 0.298; R² = 0.317) and at five shots (log-MAE = 0.251; R² = 0.452; RMSE = 1.223 g/L). Median absolute relative deviation decreased from 82.4% to 42.9% between zero and five shots. These results establish sparse, leakage-controlled calibration as a more defensible use case than unconditional prediction for unseen drugs, while identifying the need for richer molecular descriptors and external prospective validation. In practical terms, this few-shot strategy can reduce the experimental burden for a newly introduced drug by using a small screening set to calibrate a global model before mapping the remaining pressure-temperature domain.