Interpretable few-shot prediction of cross-fuel spray dynamics: experiments, empirical correlations and machine learning insights

Accurate prediction of macroscopic spray characteristics is essential for clarifying fuel-air mixing and optimizing injection strategies, yet it remains challenging for evaporating sprays at high temperature/pressure because empirical correlations transfer poorly across fuels and conventional machine-learning models are sensitive under limited, strongly coupled datasets. This study addresses whether a unified, time-resolved model can predict spray penetration, cone angle and air entrainment across diesel and methanol over varying injection pressures and ambient temperatures. A high-temperature, high-pressure spray database was established from optical experiments, spanning multiple fuels, injection pressures and ambient temperatures. Building on this database, a multi-objective prediction framework was developed and Tabular Prior-Data Fitted Network (TabPFN), a pre-trained prior model for few-shot tabular regression, was benchmarked against five conventional machine-learning models; model behavior was interpreted using SHapley Additive Prediction (SHAP). The results characterize the temporal evolution of diesel and methanol sprays and show that TabPFN consistently delivers the best performance, achieving RMSE values that are only 20-40% of those from traditional models and an R2 up to 0.99. SHAP analysis indicates physically plausible feature-attribution pathways. Overall, the main contribution is a comprehensive integration of an optical experimental database with few-shot, multi-objective learning and physics-consistent interpretability, enabling reliable cross-fuel spray prediction for injection design.