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

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 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.

Review: Machine learning for advancing low-temperature plasma modeling and simulation

“…One of the advantages of this approach is the possibility to be included in a CFD solver for solving such stiff chemically reacting problems, which can drastically reduce the computational cost. Campoli et al 199 performed state-to-state numerical simulations of high speed reacting gas flow using data-driven ML regression models. The models were applied to a system of equations for a 1D reacting flow of a five-component air mixture including a total of 122 excited states of N 2 , O 2 , NO, N, and O species with detailed vibrational kinetics.…”

“…One of the advantages of this approach is the possibility to be included in a CFD solver for solving such stiff chemically reacting problems, which can drastically reduce the computational cost. Campoli et al 199 . performed state-to-state numerical simulations of high speed reacting gas flow using data-driven ML regression models.…”

Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows

“…Their ML framework showed a great computational speed-up compared to numerical integrators, with generalization performances left unclear. Similarly, Campoli et al 39 explored different ML algorithms to regress the source terms of the ODEs system modeling the thermochemical relaxation processes. A coupling between a conventional integrator and the ML regressor was attempted, and speed-up performances were analyzed.…”

Evaluation of state-specific transport properties using machine learning methods

“…The use of machine learning methods for modeling of physical systems has grown sharply, see [Fradkov, 2022;Plotnikov et al, 2019;Fradkov and Shepeljavyi, 2022]. Machine learning methods help to accurately predict physical quantities by processing large amounts of available data, which significantly reduces computational effort and allows for implementing detailed models of physical-chemical kinetics and transport processes [Istomin and Kustova, 2021;Campoli et al, 2022;Bushmakova and Kustova, 2022]. In our preliminary studies, we used neural networks to speed up the evaluation of specific heats, thermal conductivity, and shear viscosity for single-component gases and simple mixtures, which resulted in a speed-up ratio of up to 10 3 [Istomin and Kustova, 2021].…”