Explainable machine learning and physics-constrained optimization of chalcogen catalysts for sustainable hydrogen production

of 0.961 along with low prediction error. PCO also showed better results with the highest band gap of 2.406 eV as compared with the 2.276 eV of TRBO. SHapley Additive exPlanations (SHAP) analysis also revealed the most influential descriptors that govern the behavior of the band gap, enhancing the interpretability of the model. In summary, the proposed framework offers a physically consistent, reliable, and scalable route for the discovery of new catalysts and sustainable hydrogen production.