Symbolic and domain-generalized machine learning for interpretable solubility modeling in supercritical CO₂
- 1Department of Pharmaceutics and Industrial Pharmacy, College of Pharmacy, Taif University
- 2Institute of Research and Development, Duy Tan University
Abstract
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.
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BibTeX
@article{alshehri2026symbolic,
title = {{Symbolic and domain-generalized machine learning for interpretable solubility modeling in supercritical CO₂}},
author = {Sameer Alshehri and Mahboubeh Pishnamazi},
journal = {Scientific Reports},
year = {2026},
month = jul,
doi = {10.1038/s41598-026-62721-x},
url = {https://doi.org/10.1038/s41598-026-62721-x},
note = {CC BY},
}
RIS
TY - JOUR
TI - Symbolic and domain-generalized machine learning for interpretable solubility modeling in supercritical CO₂
AU - Sameer Alshehri
AU - Mahboubeh Pishnamazi
PY - 2026
DA - 2026/07/01
JO - Scientific Reports
DO - 10.1038/s41598-026-62721-x
UR - https://doi.org/10.1038/s41598-026-62721-x
AB - 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.
SN - 2045-2322
ER -