Recent Progress in Reduced Order Models for Electromagnetic Particle-in-Cell Kinetic Plasma Simulations

We discuss recent progress on several model order reduction techniques for electromagnetic particle-in-cell (EM- PIC) simulations of kinetic plasmas: Proper Orthogonal De-composition (POD), Dynamic Mode Decomposition (DMD), and Koopman autoencoder (KAE). In the past, these techniques have been employed as powerful tools for data-driven modeling of nonlinear complex systems in general. For EMPIC kinetic plasma simulations, we show that they can reduce the number of degrees of freedom by projecting the solution space into a smaller space constituted of representative spatiotemporal modes. The trade- off between accuracy and cost can be controlled, in a tunable fashion, by adjusting the number of retained modes in the reduced model. POD, DMD, and KAE reduced order models are highly desirable to enable kinetic plasma simulations at a much reduced cost and hence more efficient parameter space sweeps during optimization loops for device design. These reduced order models are also useful as diagnosis tools for better understanding of the underlying plasma dynamics through the extraction of dominant features of the solution in a hierarchical fashion.