PreprintCC BY 4.0HAL
A neural delta-f particle-in-cell method: evolving the background with learned backward flows
Abstract
We present a novel δf particle-in-cell (PIC) method for the kinetic simulation of electrostatic plasmas in which the bulk density, acting as a control variate, is evolved using symplectic neural networks (SympNets). The SympNets are used as an approximation of the backward flow and trained using the particle trajectories. We introduce a periodic variant of the SympNet architecture that encodes the spatial periodicity of the problem into the network itself. We validate the approach with numerical results in 1D1V and 3D3V for the Vlasov-Poisson system.
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BibTeX
@misc{fournet2026neural,
title = {{A neural delta-f particle-in-cell method: evolving the background with learned backward flows}},
author = {Victor Fournet and Martin Campos Pinto and Emmanuel Franck and Victor Michel-Dansac},
howpublished = {HAL},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.30622},
eprint = {2606.30622},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05673761v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A neural delta-f particle-in-cell method: evolving the background with learned backward flows
AU - Victor Fournet
AU - Martin Campos Pinto
AU - Emmanuel Franck
AU - Victor Michel-Dansac
PY - 2026
DA - 2026/06/29
PB - HAL
DO - 10.48550/arxiv.2606.30622
UR - https://hal.science/hal-05673761v2
AB - We present a novel δf particle-in-cell (PIC) method for the kinetic simulation of electrostatic plasmas in which the bulk density, acting as a control variate, is evolved using symplectic neural networks (SympNets). The SympNets are used as an approximation of the backward flow and trained using the particle trajectories. We introduce a periodic variant of the SympNet architecture that encodes the spatial periodicity of the problem into the network itself. We validate the approach with numerical results in 1D1V and 3D3V for the Vlasov-Poisson system.
ER -