TY - JOUR

T1 - Assessment of machine learning methods for state-to-state approaches

AU - Камполи, Лоренцо

AU - Кустова, Елена Владимировна

AU - Мальцева, Полина Евгеньевна

N1 - Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2022/3/14

Y1 - 2022/3/14

N2 - 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.

AB - 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.

KW - chemical reactions

KW - machine learning

KW - neural network

KW - state-to-state kinetics

KW - vibrational relaxation

KW - REGRESSION

KW - RATE COEFFICIENTS

KW - EXCITATION

KW - ALGORITHMS

KW - MODEL

KW - RATES

KW - DISSOCIATION

KW - KINETICS

KW - DIFFUSION

UR - http://www.scopus.com/inward/record.url?scp=85127036140&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/771539d9-9bb7-3032-af22-bef4e3d0a8d1/

U2 - 10.3390/math10060928

DO - 10.3390/math10060928

M3 - Article

VL - 10

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 6

M1 - 928

ER -