Machine learning-enabled prediction of nonequilibrium reaction dynamics: A mixed Gaussian process regression–neural network framework for O + O2 state-to-state dissociation kinetics

High-temperature nonequilibrium kinetics is widely encountered in hypersonic flight and atmospheric entry. The accurate acquisition of state-to-state (StS) reaction kinetic data is crucial for constructing nonequilibrium reaction databases and high-fidelity aerodynamic simulations. However, the problem still faces great challenges due to the complex energy transfer processes. Traditional computational methods struggle to balance accuracy and efficiency in predicting StS integral cross sections (ICSs) and rate coefficients. To address this, we proposed a mixed machine learning (ML) framework, GPR-NN, combining the uncertainty-guided sampling capability of Gaussian process regression (GPR) and the strong generalization performance of neural networks (NNs) for large-scale prediction. We applied GPR-NN to the O + O2 dissociation reaction. Based on quasi-classical trajectory (QCT) calculations on the 21A' potential energy surface, a converged GPR model was constructed using 583 ICSs at a wide range of initial conditions. The dataset was expanded to train the NN model using non-redundant input features. The GPR-NN framework exhibited excellent performance: for 319 additional test points not in the training, the root-mean-square error between QCT and GPR-NN predictions was only 0.1728 Å2. The correlation coefficient R2 reached 0.9995, and the prediction time was reduced to 0.03 s. Under thermal equilibrium conditions, the model-predicted dissociation rate coefficients agreed well with experiments. The model-predicted efficiency functions demonstrate superior accuracy in quantifying vibrational nonequilibrium effects compared to empirical models. By integrating GPR's uncertainty quantification capabilities into NN training, this study overcomes the limitations of individual ML approaches and establishes a scalable and efficient strategy for ML applications in high-temperature nonequilibrium kinetics.