  Deriving governing equations of complex physical systems based on first
principles can be quite challenging when there are certain unknown terms and
hidden physical mechanisms in the systems. In this work, we apply a deep
learning architecture to learn fluid partial differential equations (PDEs) of a
plasma system based on the data acquired from a fully kinetic model. The
learned multi-moment fluid PDEs are demonstrated to incorporate kinetic effects
such as Landau damping. Based on the learned fluid closure, the data-driven,
multi-moment fluid modeling can well reproduce all the physical quantities
derived from the fully kinetic model. The calculated damping rate of Landau
damping is consistent with both the fully kinetic simulation and the linear
theory. The data-driven fluid modeling of PDEs for complex physical systems may
be applied to improve fluid closure and reduce the computational cost of
multi-scale modeling of global systems.
