Learning the Dynamics of a 1D Plasma Electrostatic Sheet Model with Graph Neural Networks*

Graph neural network-based simulators have been proposed as an alternative to model multiscale fluid and rigid body dynamics [1-3]. Their main advantages are the flexibility to operate on both mesh and particle-based simulations, the possibility of enforcing known physics constraints into the graph construction, and the capability of utilizing coarser grids and larger time steps when trained on subsampled data from high-fidelity simulations. In this talk, we explore the possibility of using this class of graph-based models to fully replace a kinetic plasma physics simulator. We show that our model learns the kinetic plasma dynamics of the one-dimensional plasma model, a predecessor of contemporary kinetic plasma simulation codes, introduced by J. Dawson [4]. Our model is capable of recovering well-known kinetic plasma processes, including plasma thermalization, electrostatic fluctuations about thermal equilibrium, and the drag on a fast sheet and a Fourier mode (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 main challenges faced to obtain the required generalization capabilities are also addressed, and possible directions for higher-dimensional surrogate models for kinetic plasmas are outlined.

[1] P. Battaglia et al., arXiv:1806.01261 (2018)

[2] A. Sanchez-Gonzalez et al., PMLR 119 (2020)

[3] T. Pfaff et al., ICLR (2021)

[4] J. Dawson, Phys. Fluids 5(4) (1962)