# A Deep Learning-Based Particle-in-Cell Method for Plasma Simulations

arXiv: https://arxiv.org/abs/2107.02232 · HTML: https://mlsanity.com/paper/2107.02232/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 24 references that are in the map.
- First posted on arXiv 5 Jul 2021.

## Builds on (most cited first, 5 of 5)

- [The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?](https://mlsanity.com/paper/2103.09655/) (2021)
- [Accelerating GMRES with Deep Learning in Real-Time](https://mlsanity.com/paper/2103.10975/) (2021)
- [Characterizing Deep-Learning I/O Workloads in TensorFlow](https://mlsanity.com/paper/1810.03035/) (2018)
- [TensorFlow Doing HPC](https://mlsanity.com/paper/1903.04364/) (2019)
- [Automatic Particle Trajectory Classification in Plasma Simulations](https://mlsanity.com/paper/2010.05348/) (2020)

## Built on by (most cited first, 4 of 4)

- [Machine Learning Applications to Computational Plasma Physics and Reduced-Order Plasma Modeling: A Perspective](https://mlsanity.com/paper/2409.02349/) (2024)
- [Learning the dynamics of a one-dimensional plasma model with graph neural networks](https://mlsanity.com/paper/2310.17646/) (2023)
- [Hamiltonian Normalizing Flows as kinetic PDE solvers: application to the 1D Vlasov-Poisson Equations](https://mlsanity.com/paper/2505.04471/) (2025)
- [Machine learning for advancing low-temperature plasma modeling and simulation](https://mlsanity.com/paper/2307.00131/) (2023)

## Abstract (arXiv)

We design and develop a new Particle-in-Cell (PIC) method for plasma simulations using Deep-Learning (DL) to calculate the electric field from the electron phase space. We train a Multilayer Perceptron (MLP) and a Convolutional Neural Network (CNN) to solve the two-stream instability test. We verify that the DL-based MLP PIC method produces the correct results using the two-stream instability: the DL-based PIC provides the expected growth rate of the two-stream instability. The DL-based PIC does not conserve the total energy and momentum. However, the DL-based PIC method is stable against the cold-beam instability, affecting traditional PIC methods. This work shows that integrating DL technologies into traditional computational methods is a viable approach for developing next-generation PIC algorithms.