Do Graph Neural Networks Dream of Landau Damping? Insights from Kinetic Simulations of a Plasma Sheet Model

We explore the possibility of fully replacing a plasma physics kinetic simulator with a graph neural network-based simulator. We focus on this class of surrogate models given the similarity between their message-passing update mechanism and the traditional physics solver update, and the possibility of enforcing known physical priors into the graph construction and update. We show that our model learns the kinetic plasma dynamics of the one-dimensional plasma model, a predecessor of contemporary kinetic plasma simulation codes, and recovers a wide range of well-known kinetic plasma processes, including plasma thermalization, electrostatic fluctuations about thermal equilibrium, and the drag on a fast sheet and Landau damping. We compare the performance against the original plasma model in terms of run-time, conservation laws, and temporal evolution of key physical quantities. The limitations of the model are presented and possible directions for higher-dimensional surrogate models for kinetic plasmas are discussed.