Non-linear control variate in δf particle-in-cell methods using symplectic neural networks

Victor Fournet; Martin Campos Pinto; Emmanuel Franck; Victor Michel-Dansac

Non-linear control variate in δf particle-in-cell methods using symplectic neural networks

Computational Physics 2026-06-29 v1

Authors: Victor Fournet , Martin Campos Pinto , Emmanuel Franck , Victor Michel-Dansac

Abstract

We present a novel {\delta}f 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.

Keywords

particle-in-cell delta-f method symplectic neural networks control variate Vlasov-Poisson electrostatic plasma

Cite

@article{arxiv.2606.30622,
  title  = {Non-linear control variate in δf particle-in-cell methods using symplectic neural networks},
  author = {Victor Fournet and Martin Campos Pinto and Emmanuel Franck and Victor Michel-Dansac},
  journal= {arXiv preprint arXiv:2606.30622},
  year   = {2026}
}