Interpretable and highly accurate tertiary tree-based ensemble hybrid models for the prediction of photocurrent density and electrode potential in PEC cell: Theoretically supported and externally validated by experimental data

Photocurrent density (J) and potential with respect to reverse hydrogen electrode (VRHE) are crucial parameters for evaluating the performance of a PEC system for green hydrogen production. The study aims to create a highly accurate, interpretable, robust and versatile machine learning model for the prediction of J and VRHE supported by theory and external validation. In this study, at first, we developed two binary hybrid models (M3, M4) by using BO optimized two single models (M1, M2) and a dataset of 2593 records followed by the development of two tertiary hybrid models (M5, M6) for J and VRHE prediction. The generalizability of all models was assessed applying external validation (EV) technique using five experimental datasets and three physics-based models (PBM) (P1-3) for J. The SHAP technique was utilized to explain the features contribution in hybrid and single models for J and VRHE prediction. In the prediction of J, M4, M5 and M6 achieved the best ever accuracy in terms of R2>0.977 (best ever reported accuracy) and M5, M6 achieved the highest among all with R2 > 0.999. M5 was found to the best generalized models among all models. Interestingly, P3 was found to be the best correlated PBM with all ML based models. Further, the best ever accuracy in terms of R2 >0.999 was achieved for VRHE prediction (best ever reported value of R2=0.712). In EV of VRHE using five unseen experimental datasets, M6 was the best performing model. In the prediction of J and VRHE, the contribution of each feature for single and hybrid models were established using SHAP technique. Bandgap, electrode area, experimental potential were found within the top six influencing parameters in J prediction. Experimental potential was found within the top three influencing features in VRHE prediction. Further, the success of tertiary models was well explored using multiple statistical techniques.