Partition-of-unity flow-based solver for kinetic plasma simulations

We introduce a novel flow-based solver for kinetic plasma simulations. Unlike Particle-in-Cell (PIC) methods that evolve particle weights ( f_id z ), our solver directly tracks the distribution function values ( f_i ) at specific phase-space points, or markers, providing an accurate point-wise representation. Unlike conventional semi-Lagrangian schemes, we maintain continuous marker trajectories along with the update of f_i and employ a Partition-of-Unity weighting to reconstruct macroscopic quantities without solving computationally expensive large linear systems. Validation shows our method achieves accuracy comparable to PIC while using 100 times fewer markers and reducing the computational wall time. The framework’s direct connection to Continuous Normalizing Flows opens promising avenues for developing hybrid physics-machine learning approaches.