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.