Physics-informed hybrid machine learning for predicting effects of metal oxide nano additives on performance and emissions of biodiesel-fueled engines

Accurate prediction of the performance and emission characteristics of nanoparticle-enhanced biodiesel-fueled compression ignition engines is essential for efficient engine optimization, cleaner combustion, and reducing experimental costs and time. This study integrates combustion physics with stacked ensemble learning to develop a physics-informed Bayesian-optimized hybrid (PIBoH) framework to simultaneously predict brake thermal efficiency (BTE), brake-specific fuel consumption (BSFC), hydrocarbon (HC), carbon monoxide (CO), and nitrogen oxide (NO x ) emissions. A comprehensive experimental database was compiled from published studies covering diverse biodiesel feedstocks, metal oxide nanoparticles, and engine operating conditions. To embed domain knowledge into the learning process, conventional categorical descriptors were replaced with physically meaningful fuel-property variables, a quantitative additive overall effectiveness index, and seven physics-informed engineered features. Bayesian optimization was employed to fine-tune hyperparameters of the PIBoH framework. The designed framework predicted 298 datasets with average absolute relative deviations of 4.48%, 3.44%, 5.42%, 6.63%, and 5.30% for BTE, BSFC, HC, CO, and NO x , respectively, corresponding to coefficients of determination of 0.9543, 0.9808, 0.9924, 0.9934, and 0.9901. Applicability-domain analysis further demonstrated reliable prediction stability across the investigated operating conditions. SHapley Additive exPlanations (SHAP) analysis identified fuel density and engine load as the dominant variables governing both engine performance and pollutant formation.