Uncertainty-aware machine learning-based prediction of plasma parameters in a microwave atmospheric pressure plasma jet

Abstract

Microwave atmospheric pressure plasma jets (MW-APPJs) exhibit significant potential for diverse applications, i.e., hydrogen production, CO₂ dissociation, water treatment, material processing and waste treatment due to their stable operation at atmospheric pressure and generation of highly tunable reactive species. For effective utilization of MW-APPJs, a detailed understanding of the operational conditions that influence plasma parameters is essential. The present work proposes an uncertainty-aware, multi-output, interpretable supervised machine learning (ML) framework to predict eight plasma parameters, viz. electron excitation temperature (T_exc), electron number density (n_e), four reactive species (OH, N₂, H_α and O), gas temperature (T_g), and plume length. A dataset comprising 441 experimental runs was generated by varying the input powers (700–1000 W), sliding short positions (0.95–1.05λ_g/2) and argon flow rate (5–15 lpm). Six regression models, namely k-nearest neighbours (KNN), extra trees (ET), random forest (RF), artificial neural networks (ANN), gradient boosting (GB), and extreme gradient boosting (XGB), were optimized using Bayesian hyperparameter tuning and evaluated using both accuracy and reliability metrics. While XGB achieved competitive pointwise accuracy, the optimized GB model emerged as the most balanced performer when predictive accuracy, calibration behaviour, and uncertainty reliability were jointly considered. On a held-out test set, the GB model achieved mean absolute percentage errors below 3% and R² values exceeding 0.97 across all plasma parameters. Bootstrap-based uncertainty quantification demonstrated near-nominal 90% prediction interval coverage with comparatively narrow uncertainty bounds, and calibration analysis confirmed statistically consistent uncertainty estimates. Experimental validation using 30 independent plasma operating conditions, separated into interpolated and extrapolated regimes, further confirmed robust generalization, with increased epistemic uncertainty appropriately accompanying extrapolative predictions. SHapley Additive exPlanations (SHAP) based interpretability analysis identified microwave power as the dominant controlling feature for most plasma parameters, while gas flow rate governed the intensity of OH emission. Overall, this uncertainty-aware ML framework provides a reliable foundation for data-driven plasma diagnostics and future optimization of MW-APPJ-based processes.