  It is well known that numerical simulations of high-speed reacting flows, in
the framework of state-to-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-of-the-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 one-dimensional
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.
