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International Journal of Statistics and Data Science

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ArticleOpen Access http://dx.doi.org/10.26855/ijsds.2026.06.004

Deep Neural Network Surrogate Modeling of the Electron Boltzmann Equation for Low-temperature Plasma Kinetics

Mohammad Yaghoub Abdollahzadeh Jamalabadi

Department of Mechanical Engineering, Chabahar Maritime University, Chabahar 99717, Iran.

*Corresponding author: Mohammad Yaghoub Abdollahzadeh Jamalabadi

Published: June 16, 2026

Abstract

Low-temperature plasma simulations face a fundamental trade-off between computational efficiency and physical accuracy when describing kinetic electron effects. The electron energy distribution function (EEDF) is commonly assumed to be Max-wellian for simplicity, yet real plasmas frequently exhibit non-equilibrium EEDFs that substantially alter transport coefficients and reaction rates. This work presents a hybrid framework that integrates a deep neural network (DNN) surrogate, trained on solutions of the two-term Boltzmann equation, into spatially resolved fluid plasma simulations. The DNN predicts electron-impact rate constants, reduced mobility, effective collision frequency, and a field coefficient as explicit functions of three local parameters: mean electron energy, ionization degree, and excited-state mole fraction. Applied to an inductively coupled plasma (ICP) reactor in argon, the surrogate reduces the computational cost of a fully coupled Boltzmann-fluid simulation from approximately one hour to ten minutes—a six-fold speedup for the specific time-dependent case studied—while faithfully capturing non-Maxwellian kinetic effects that a Maxwellian model misses entirely (e.g., 22% deviation in electron temperature and 28% in excited state density under the conditions examined). The proposed approach provides a practical and generalizable pathway for incorporating rigorous electron kinetics into multidimensional plasma models without prohibitive overhead, potentially enabling more accurate simulations for reactor design and process optimization.

Keyword

Deep neural network surrogate; Electron Boltzmann equation; Low-temperature plasma kinetics; Electron energy distribution function; Non‑Maxwellian plasmas; Physics‑informed machine learning; Inductively coupled plasma modeling

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Copyright

© 2026 by the author(s).
This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) license, which permits non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited and is not modified or adapted.
https://creativecommons.org/licenses/by-nc-nd/4.0/

How to cite this paper

Deep Neural Network Surrogate Modeling of the Electron Boltzmann Equation for Low-temperature Plasma Kinetics

How to cite this paper: Mohammad Yaghoub Abdollahzadeh Jamalabadi. (2026). Deep Neural Network Surrogate Modeling of the Electron Boltzmann Equation for Low-temperature Plasma Kinetics. International Journal of Statistics and Data Science2(1), 44-72.

DOI: http://dx.doi.org/10.26855/ijsds.2026.06.004