Machine-learning heat flux closure for multi-moment fluid modeling of nonlinear Landau damping

Nonlinear plasma physics problems are usually simulated through comprehensive modeling of phase space. The extreme computational cost of such simulations has motivated the development of multi-moment fluid models. However, a major challenge has been finding a suitable fluid closure for these fluid models. Recent developments in physics-informed machine learning have led to a renewed interest in constructing accurate fluid closure terms. In this study, we take an approach that integrates kinetic physics from the first-principles Vlasov simulations into a fluid model (through the heat flux closure term) using the Fourier neural operator-a neural network architecture. Without resolving the phase space dynamics, this new fluid model is capable of capturing the nonlinear evolution of the Landau damping process that exactly matches the Vlasov simulation results. This machine learning-assisted new approach provides a computationally affordable framework that surpasses previous fluid models in accurately modeling the kinetic evolution of complex plasma systems.