A Deep Neural Network Model for Thermochemical Equilibrium Prediction in Diesel Combustion with Uncertainty Quantification and Explainability

Deep neural networks (DNNs) have demonstrated remarkable capability in accurately predicting equilibrium combustion products and thermodynamic properties of diesel combustion. However, the lack of awareness of uncertainty and interpretability has limited their scientific credibility and practical application. In this work, an enhanced DNN framework with uncertainty quantification and explainability is developed. The model achieves high accuracy across all outputs, with R2 values exceeding 0.99 for major thermodynamic variables. In this model, Monte Carlo dropout sampling is used to estimate epistemic uncertainty, and prediction confidence intervals are analyzed across all species and thermodynamic outputs, revealing strong correlations for major components. Model explainability is further explored using Shapley additive explanations (SHAP), which attribute the influence of equivalence ratio, temperature, and pressure on each predicted species and combustion characteristics. The combined uncertainty quantification and explainability framework not only enhances confidence in DNN combustion models but also provides physical insight into the relationships between input conditions and equilibrium thermochemistry that are learned by the DNN.