Fourier-enhanced separable physics-informed neural networks for plasma kinetic simulations

Abstract

Kinetic equations of plasma are often characterized by high dimensionality, multiscale behavior and strong nonlinearity. In recent years, physics-informed neural networks (PINNs) have attracted considerable attention as a novel numerical method for solving partial differential equations. However, the application of standard PINNs still faces challenges, including spectral bias, relatively high consumption of GPU memory, low training efficiency, and training failure over long time intervals. To address these difficulties, this work uses an enhanced PINN computational framework and systematically evaluates its performance on a range of representative benchmark problems, including those described by electrostatic Vlasov systems and reduced models. Specifically, a separable physics-informed neural network architecture is employed to reduce memory usage and training time in solving kinetic equations; Fourier features are introduced to enhance the representation of high-frequency components and fine phase-space structures; strategies such as time marching, transfer learning, and hard constraint of initial conditions are incorporated to enable long-time phase-space evolution simulations. Based on this framework, a variety of electrostatic kinetic problems in both unmagnetized and magnetized plasmas are investigated, including Landau damping, ion-acoustic waves, Bernstein modes, linear and nonlinear beam instabilities, diocotron instability and the ion-temperature-gradient mode in tokamak. Numerical results show that the improved PINN method can accurately capture time evolution of the distribution function and electric field, which are consistent with theoretical analysis and conventional numerical codes. These findings demonstrate the potential of enhanced PINNs as complementary numerical frameworks for the electrostatic kinetic problems considered in this work.