Stochastic operator learning for chemistry in non-equilibrium flows

This work introduces a novel framework that combines physically consistent model error characterization with spectral expansions-based operator learning for reduced-order models of non-equilibrium chemical kinetics, ultimately leading to a stochastic operator learning approach. By leveraging the Bayesian framework, we identify and infer sources of model error and parametric uncertainty within the coarse-graining methodology (CGM) across a range of initial conditions. The model error is embedded into the chemical kinetics model to ensure that its propagation to quantities of interest remains physically consistent. For operator learning, we develop a methodology that separates temporal dynamics from the parameters governing initial conditions, model error, and parametric uncertainty. Karhunen-Loève expansion (KLE) is employed to capture temporal dynamics, yielding temporal modes, while polynomial chaos expansion (PCE) is subsequently used to map model error and input parameters to the KLE coefficients. This proposed model offers three significant advantages: i) Separating the temporal dynamics from other inputs ensures the stability of the chemistry surrogate when coupled with fluid solvers; ii) The framework fully accounts for model and parametric uncertainty, enabling robust probabilistic predictions; iii) The surrogate model is highly interpretable, with visualizable temporal modes and a PCE component that facilitates the analytical calculation of sensitivity indices, allowing for the ranking of input parameter influence. We apply this framework to the $O_2-O$ chemistry system under hypersonic flight conditions, validating it in both a 0-D adiabatic reactor and coupled simulations with a fluid solver in a 1-D normal shock test case. Results demonstrate that the surrogate is stable during time integration, delivers physically consistent probabilistic predictions accounting for both model and parametric uncertainty, and achieves a maximum relative error below 10 %. This work represents a significant step forward in enabling probabilistic predictions of non-equilibrium chemical kinetics within coupled fluid solvers, offering a physically accurate approach for hypersonic flow predictions.