Abstract: In the developed particle-in-cell/Monte Carlo collision (PIC/MCC) model, the iterative solution of Poisson’s equation dominates computational resource consumption, while parallelization has optimized other components. To reduce these costs, neural networks are introduced for accelerating field solvers. However, direct solutions by neural networks exhibit significant performance degradation under noisy conditions, which requires increased particle counts and substantially increases particle-pushing runtime. To overcome this limitation, we propose physics-informed neural networks (PINNs) for estimating initial conditions and use iterative solutions for smoothing noise. Furthermore, a novel hybrid method that integrates PINNs with multigrid methods is developed, achieving accelerated convergence and enhanced computational efficiency. Benchmark test results are then presented to validate both the Poisson solver and the integrated PIC/MCC framework. These results advance plasma physics research, thus providing guidance for plasma source design aimed at process optimization.