Reduced Models for Plasmas: Integration of "particle-in-cell" Simulations and Machine Learning

Accurate reduced models are essential to describe plasma dynamics across scales while maintaining computational feasibility for large-scale simulations. These models require closure relations that connect macroscopic fluid quantities to the underlying kinetic behaviour, and recent data-driven approaches have shown potential for deriving such relations directly from kinetic simulations.

In this work, a sparse-regression framework based on the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm is adapted to infer fluid equations from fully kinetic OSIRIS Particlein-Cell simulations. The method is first benchmarked using the two-stream instability, extending previous work by accurately reconstructing the hierarchy of fluid moments up to the third-order equation.

Using both the two-stream instability and a linear electron–plasma–wave configuration, we assess under which conditions sparse regression recovers the hierarchy of fluid equations with a waterbag closure and identify its limits as non-linear phase mixing develops. We show that sparse regression can extract compact and physically interpretable reduced plasma models directly from kinetic simulations, providing a data-driven path toward machine-learned closures applicable to future relativistic and hybrid plasma studies.