Physics-informed low-temperature plasma simulation: frameworks and applications*

The rapid development of artificial intelligence (AI) provides us new and powerful tools for computational plasma physics. At the same time, incorporating the laws of physics into data-driven models has become a new paradigm for plasma simulation. Physics-informed neural networks (PINN) are one of the methods that can seamlessly integrate physical knowledge and data. In the past few years, we have proposed four general physics-informed frameworks for low-temperature plasma simulation, namely, Coefficient-Subnet Physics-Informed Neural Network (CS-PINN), Runge-Kutta Physics-Informed Neural Network (RK-PINN), Meta Physics-Informed Neural Network (Meta-PINN), and Neural Architecture Search-guided Physics-Informed Neural Network (NAS-PINN). CS-PINN uses either a neural network or an interpolation function as the subnet to approximate solution-dependent coefficients (e.g. electron-impact cross sections, thermodynamic properties, transport coefficients, et al.) 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. To reduce the training time of PINN-based plasma simulation, Meta-PINN is trained by a two-loop optimization on various training tasks of plasma modeling, and then used to initialize the PINN-based network for new tasks. Considering that the design of neural network structure basically relies on prior knowledge and experience, NAS-PINN is proposed to automatically search the optimum neural architecture for solving certain PDEs including plasma equations. Apart from PINN-based simulation, we are also developing operator learning and federated learning-based plasma simulation framework. All the simulation frameworks are demonstrated on 1D or 2D cases. All the results show the great potential for the application of AI in plasma simulation.