Göttingen 2025 – wissenschaftliches Programm
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P: Fachverband Plasmaphysik
P 10: Poster Session I
P 10.18: Poster
Dienstag, 1. April 2025, 16:15–18:15, ZHG Foyer 1. OG
Solving the Spatially Dependent Boltzmann Equation for Electrons with Physics-Informed Neural Networks — •Ihda Chaerony Siffa1, Detlef Loffhagen1, Markus M. Becker1, and Jan Trieschmann2 — 1Leibniz Institute for Plasma Science and Technology (INP), Felix-Hausdorff-Straße 2, 17489 Greifswald, Germany — 2Kiel University, Kaiserstraße 2, 24143 Kiel, Germany
Physics-informed neural networks (PINNs) are an exciting new research area in the field of scientific machine learning. They offer an alternative approach to numerically solving partial differential equations (PDEs) in both forward and inverse problem settings with great flexibility. This study investigates the application of PINNs to solve the spatially one-dimensional electron Boltzmann equation in two-term approximation, which is relevant for the study of non-local effects in weakly ionized, non-thermal plasmas. An attention-based neural network architecture is developed to prevent the convergence to incorrect or trivial solutions of the PDEs as encountered by other architectures in solving this kinetic equation. Numerical experiments are conducted for argon plasmas considering homogeneous electric fields with varying values using a conventional numerical method and the PINN approach. The results from PINNs show good agreement with the reference solutions (obtained from the conventional approach) for the considered cases, which further strengthens PINNs' position as an alternative to solve this type of equation, paving a way for more efficient and accurate fluid-Poisson plasma simulations.
Keywords: Machine learning; 1D electron Boltzmann equation; PINNs; Weakly ionized plasmas