Data-driven, multi-moment fluid modeling of Landau damping using machine learning

Kinetic approaches are generally accurate in dealing with microscale plasma physics problems but are computationally expensive for large-scale and multi-scale systems. One of the long-standing problems in plasma physics is the integration of kinetic effects into fluid models, which is often achieved through analytical closure terms. In this work, data-driven approaches are adopted to incorporate fluid closures in a multi-moment fluid model, and consequently, it can accurately capture the collisionless Landau damping. We investigate two different machine learning approaches 1) the mPDE-Net architecture with an explicitly formulated fluid closure and 2) the physics-informed neural network (PINN) with an implicit fluid closure. The learned multi-moment fluid models are constructed from and tested against fully kinetic Vlasov simulation data. The newly constructed fluid models can successfully capture the time evolution of the electric field energy, including its damping rate. This work sheds light on the accurate and efficient modeling of large-scale systems, which can be extended to complex multiscale laboratory, space, and astrophysical plasma physics problems.