Greifswald 2024 – scientific programme
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P: Fachverband Plasmaphysik
P 11: Codes and Modeling I
P 11.3: Talk
Tuesday, February 27, 2024, 17:25–17:40, ELP 6: HS 3
Solving the Parametric Boltzmann Equation for Electrons Using Physics-Informed Neural Networks — •Ihda Chaerony Siffa1, Detlef Loffhagen1, Markus M. Becker1, and Jan Trieschmann2 — 1Leibniz Institute for Plasma Science and Technology (INP), Greifswald, Germany — 2Kiel University, Kiel, Germany
The coupling of fluid-Poisson models for low-temperature plasma simulations with the Boltzmann equation of electrons is often needed to ensure the reliability of such models. A direct coupling is, however, often too expensive with respect to calculation time. The pre-calculation of look-up tables for the electron transport and rate coefficients as a function of the reduced electric field strength or mean electron energy is therefore a common practice. In this work, we present a way to parametrically solve the electron Boltzmann equation in two-term approximation using the so-called Physics-Informed Neural Networks (PINNs). PINNs are a mesh-free method and provide differentiable solutions with the potential to ultimately predict electron properties more efficiently than traditional Boltzmann solvers. Presently, the artificial neural network surrogate model takes into account two inputs, the kinetic energy of electrons and an additional input parameter, which represents either the reduced electric field or the mean electron energy, and outputs the isotropic component of the electron velocity distribution function. This contribution discusses the advantages and limitations of the present approach, and gives an outlook for future work.
Keywords: Machine Learning; Electron Boltzmann Equation; PINNs; LTP