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

Abstract

Plasma simulation is an important, and sometimes the only, approach to investigating plasma behavior. In this work, we propose two general artificial-intelligence-driven frameworks for low-temperature plasma simulation: Coefficient-Subnet Physics-Informed Neural Network (CS-PINN) and Runge-Kutta Physics-Informed Neural Network (RK-PINN). 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, etc.) in plasma equations. Based on this, 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 spatiotemporal space to the equation's solution. Based on these two frameworks, we demonstrate preliminary applications in 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, RK-PINN has the ability to yield a good solution for transient plasma simulation with not only large time steps but also limited noisy sensing data.