Integrating Kinetic Effects into Multi-Moment Fluid Models through Machine Learning

Kinetic approaches are generally accurate for modeling microscale plasma physics but are computationally expensive for large-scale and multiscale systems. A long-standing challenge in plasma physics is the integration of kinetic effects into fluid models, typically achieved through analytical closure terms. In this work, we adopt data-driven methods to learn fluid closures from kinetic simulation data within a multi-moment fluid framework, enabling accurate reproduction of kinetic phenomena such as collisionless Landau damping. We explore several machine learning techniques, including sparse regression, Physics-Informed Neural Networks (PINNs), and Fourier Neural Operators (FNOs). These learned fluid models successfully capture the time evolution of the electric field energy, including accurate representation of damping rates. This approach offers a promising path toward efficient and accurate modeling of large-scale plasma systems and is extensible to complex multiscale phenomena such as magnetic reconnection.