# Learning the dynamics of a one-dimensional plasma model with graph neural networks

arXiv: https://arxiv.org/abs/2310.17646 · HTML: https://mlsanity.com/paper/2310.17646/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 17 references that are in the map.
- First posted on arXiv 26 Oct 2023.

## Builds on (most cited first, 9 of 9)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
- [Learning rigid dynamics with face interaction graph networks](https://mlsanity.com/paper/2212.03574/) (2022)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [A Deep Learning-Based Particle-in-Cell Method for Plasma Simulations](https://mlsanity.com/paper/2107.02232/) (2021)

## Built on by (most cited first, 2 of 2)

- [Learning collision operators from plasma phase space data using differentiable simulators](https://mlsanity.com/paper/2601.10885/) (2026)
- [Deterministic and probabilistic neural surrogates of global hybrid-Vlasov simulations](https://mlsanity.com/paper/2601.12614/) (2026)

## Abstract (arXiv)

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.