State-to-state numerical simulations of high-speed reacting flows are the most detailed but also often prohibitively computationally expensive. In this work, we explore the usage of machine learning algorithms to alleviate such a burden. Several tasks have been identified. Firstly, data-driven machine learning regression models were compared for the prediction of the relaxation source terms appearing in the right-hand side of the state-to-state Euler system of equations for a one-dimensional reacting flow of a N2/N binary mixture behind a plane shock wave. Results show that, by appropriately choosing the regressor and opportunely tuning its hyperparameters, it is possible to achieve accurate predictions compared to the full-scale state-to-state simulation in significantly shorter times. Secondly, several strategies to speed-up our in-house state-to-state solver were investigated by coupling it with the best-performing pre-trained machine learning algorithm. The embedding of machine learning algorithms into ordinary differential equations solvers may offer a speed-up of several orders of magnitude. Nevertheless, performances are found to be strongly dependent on the interfaced codes and the set of variables onto which the coupling is realized. Finally, the solution of the state-to-state Euler system of equations was inferred by means of a deep neural network by-passing the use of the solver while relying only on data. Promising results suggest that deep neural networks appear to be a viable technology also for this task.

It is well known that numerical simulations of high-speed reacting flows, in the framework of stateto-state formulations, are the most detailed but also often prohibitively computationally expensive. In this work, we start to investigate the possibilities offered by the use of machine learning methods for state-to-state approaches to alleviate such burden. In this regard, several tasks have been identified. Firstly, we assessed the potential of state-ofthe-art data-driven regression models based on machine learning to predict the relaxation source terms which appear in the right-hand side of the state-to-state Euler system of equations for a onedimensional reacting flow of a N 2 /N binary mixture behind a plane shock wave. It is found that, by appropriately choosing the regressor and opportunely tuning its hyperparameters, it is possible to achieve accurate predictions compared to the full-scale state-to-state simulation in significantly shorter times. Secondly, we investigated different strategies to speed-up our in-house state-to-state solver by coupling it with the best-performing pre-trained machine learning algorithm. The embedding of machine learning methods into ordinary differential equations solvers may offer a speed-up of several orders of magnitude but some care should be paid for how and where such coupling is realized. Performances are found to be strongly dependent on the mutual nature of the interfaced codes. Finally, we aimed at inferring the full solution of the state-to-state Euler system of equations by means of a deep neural network completely by-passing the use of the state-to-state solver while relying only on data. Promising results suggest that deep neural networks appear to be a viable technology also for these tasks.