Applications of physics-informed neural networks to elucidating electron swarm transport in plasmas

In order to optimize plasmas for many and various applications, electron transport coefficients are valuable information. Furthermore, electron transport coefficients are inevitable for simulating plasmas and validating electron collision cross sections, which are required in particle-based simulations and the Boltzmann equation analysis; therefore, reliable electron transport coefficients are highly required. The Boltzmann equation analysis and electron swarm experiments are methods for obtaining electron transport coefficients. Physics-informed neural networks (PINNs) have recently emerged as a new approach to solving partial differential equations [1]. PINNs also allow us to find the governing equation from numerical data. This is called “Data-driven discovery of partial differential equations.” In this talk, we will show applications of PINNs in the Boltzmann equation analysis and electron swarm experiments [2–4]. In the former application, PINNs are utilized to solve the electron Boltzmann equation. An artificial neural network is employed to represent a solution to the equation, namely the electron velocity distribution function (EVDF). The PINNs allow us to solve the Boltzmann equation without expanding the EVDF in orthogonal functions; therefore, we can obtain an accurate EVDF. In the latter application, we discover the electron continuity equation from measured spatiotemporal development of an electron swarm under DC electric fields. The coefficients appearing in the continuity equation are treated as tunable parameters and then optimized such that a solution of the continuity equation, namely the spatiotemporal profile of the electron swarm, matches the measured data. We can determine electron transport coefficients from the optimized parameters. The ionization collision frequency, bulk electron drift velocity, longitudinal diffusion coefficient, and so on in Ar gas were determined from the measured data [5] and compared with those calculated from electron collision cross sections of Ar gas.