DFT-Based fuzzy topological indices integrated with machine learning for accurate prediction of topical drug properties

In this study, we developed a novel framework to predict the physicochemical properties of topical drugs by integrating fuzzy topological indices with machine learning (ML) models. The chemical structures of the selected drugs were optimized using Gaussian software, and both bond lengths (edges) and vertex properties, corresponding to the atomic masses of each molecule, were fuzzified through Density Functional Theory (DFT). Fuzzy topological indices (FTIs) were then calculated to capture the relationships between molecular geometry, atomic composition, and topological features. Two machine learning algorithms, Linear Regression (LR) and optimized Support Vector Regression (SVR-Tuned), were employed for property prediction. The models were trained on the main dataset and validated on additional test drugs excluded from training, enabling a rigorous assessment of generalization, predictive accuracy, and the absence of overfitting. The results showed that the proposed fuzzy QSPR framework, combined with optimized, achieves high predictive performance, robustness, and strong generalization. This methodology provides an efficient computational tool for estimating molecular properties and can support the rational design of next-generation topical pharmaceutical agents.