Latent Residual-Closure Fourier Neural Operator for Robust Multi-Field Solving in Particle-in-Cell Simulations

Abstract

Particle-in-cell (PIC) simulations are widely used for kinetic plasma modeling in energy applications, but their efficiency is often limited by repeated field solves on dense meshes. This work proposes a Latent Residual-Closure Fourier Neural Operator (LRC-FNO) for robust surrogate multi-field solving in PIC simulations. Rather than treating field prediction as a purely data-driven regression task, LRC-FNO formulates PIC field solving as a two-level residual-closure problem involving source compression and source-to-field operator mapping. An autoencoder extracts compact representations of particle-deposited source fields, while a Latent Closure Refiner recovers unresolved residual structures lost during compression. A Coarse-FNO Solver captures the dominant field response, and a Residual-Closure FNO restores full-resolution corrections. The method is tested on three benchmarks with increasing complexity: 1D linear Landau damping (LLD), 2D two-stream instability (TSI), and a 2D scrape-off layer (SOL) fusion plasma model. In LLD and TSI, LRC-FNO better preserves charge-to-potential mapping, potential-mode evolution, residual charge structures, and particle-field energy exchange during closed-loop PIC integration. In the SOL case, LRC-FNO achieves relative L2 errors of 0.0447 for the self-consistent potential and 0.0251 for the magnetic vector potential in single-step prediction. More importantly, when used as a neural initial guess with 20 iterative corrections, LRC-FNO maintains strong physical consistency in extrapolated closed-loop simulations, preserving charge and current density structures over a time range close to twice the training horizon. These results demonstrate that LRC-FNO can serve as both a fast surrogate field solver and a high-quality initialization strategy for iterative PIC field solvers.