Non-linear control variate in δf particle-in-cell methods using symplectic neural networks
This work addresses the need for efficient variance reduction in plasma simulations, offering a novel integration of machine learning with traditional PIC methods.
The paper introduces a δf particle-in-cell method that uses symplectic neural networks to evolve the control variate, achieving accurate kinetic simulations of electrostatic plasmas. Numerical validation in 1D1V and 3D3V shows the method's effectiveness.
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.