Low-temperature plasma simulation based on physics-informed neural networks: frameworks and preliminary applications

Plasma simulation is an important and sometimes only approach to investigating plasma behavior. In this work, we propose two general AI-driven frameworks for low-temperature plasma simulation: Coefficient-Subnet Physics-Informed Neural Network (CS-PINN) and Runge-Kutta Physics-Informed Neural Network (RK-PINN). The CS-PINN uses either a neural network or an interpolation function (e.g. spline function) as the subnet to approximate solution-dependent coefficients (e.g. electron-impact cross sections, thermodynamic properties, transport coefficients, et al.) in plasma equations. On the basis of this, the RK-PINN incorporates the implicit Runge-Kutta formalism in neural networks to achieve a large-time-step prediction of transient plasmas. Both CS-PINN and RK-PINN learn the complex non-linear relationship mapping from spatio-temporal space to equation's solution. Based on these two frameworks, we demonstrate preliminary applications by four cases covering plasma kinetic and fluid modeling. The results verify that both CS-PINN and RK-PINN have good performance in solving plasma equations. Moreover, the RK-PINN has ability of yielding a good solution for transient plasma simulation with not only large time step but also limited noisy sensing data.