Towards Efficient Simulations of Non-Equilibrium Chemistry in Hypersonic Flows: A Physics-Informed Neural Network Framework

Simulating non-equilibrium hypersonic flows by relying on high fidelity state-to-state kinetics is computationally intensive. The cost is determined by the high computational load associated with the solution of underlying master equations, which predict the evolution of the species mass fractions and the rovibrational distribution functions by considering energy exchange and dissociation processes. In this work, a machine learning (ML)-based approach is developed for accelerating numerical simulations of such computationally expensive flows. A physics-informed DeepONet (PI-DeepONet), i.e. a deep operator network (DeepONet) trained in the physics-informed (PI) fashion, is constructed to learn the solution operator of coarse-grained (CG) kinetic master equations. Based on this approach, the coarse-grained description reduces the dimensionality of the stiff master equations, while the ML-based surrogation bypasses their numerical integration. Simultaneously, the physics-informed attribute of the ML model, given by appropriate choices of loss functions, constraints, and inference algorithms, enforces predictions that respect the underlying non-equilibrium physics. The proposed framework is meant to investigate rovibrational relaxations and dissociation of gas mixtures, and it is here tested on the O₂-O mixture. The novel ML tool outperforms the numerical integrators by two orders of magnitude in speedup with an error smaller than 2%. This work lays the foundation for an efficient ML- and CG-based surrogation to be coupled with CFD simulations for accurately characterizing the thermochemical non-equilibrium.