Enhanced physics-informed neural networks for Vlasov–Poisson simulations

Kinetic theory is one of the fundamental descriptions in plasma physics. Large-scale numerical simulations for kinetic models such as the non-relativistic Vlasov–Poisson system and the Vlasov–Maxwell system are computationally demanding. To save computer resources, this work uses physics-informed neural network (PINN) and its variant separable PINN (SPINN) to approach the Vlasov–Poisson system. We constructed PINN and SPINN solvers for the multi-dimensional Vlasov–Poisson system and implemented the simulation of Landau damping and two-stream instabilities. The SPINN is proved to be effective for approaching high-resolution and high-dimensional solutions because of its fast training and low memory consumption, especially in capturing linear Landau damping in six-dimensional phase space. In this work, these AI solvers show potential in balancing computational cost, effectiveness and efficiency for direct Vlasov simulations. Therefore, they are expected to be useful in kinetic simulation for fusion plasma, astrophysical plasma and related applications.