Assessment of Machine Learning Methods for State-to-State Approach in Nonequilibrium Flow Simulations

Lorenzo Campoli, Elena Kustova and Polina Maltseva
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Lorenzo Campoli: Department of Fluid Mechanics, Saint Petersburg State University, 7/9 Universitetskaya nab., 199034 St. Petersburg, Russia
Elena Kustova: Department of Fluid Mechanics, Saint Petersburg State University, 7/9 Universitetskaya nab., 199034 St. Petersburg, Russia
Polina Maltseva: Department of Fluid Mechanics, Saint Petersburg State University, 7/9 Universitetskaya nab., 199034 St. Petersburg, Russia

Mathematics, 2022, vol. 10, issue 6, 1-21

Abstract: 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 N 2 /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.

Keywords: machine learning; neural network; state-to-state kinetics; vibrational relaxation; chemical reactions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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