We extend the recently developed entropic and conservative variance reduction framework [M. Sadr, N. G. Hadjiconstantinou, A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction, Journal of Computational Physics 472 (2023) 111677.] to the particle-in-cell (PIC) method of solving Vlasov-Poisson equation. We show that a zeroth-order approximation that freezes the importance weights during the velocity-space kick is stable at the expense of introducing bias. Then, we propose a correction for the weight distribution using maximum cross-entropy formulation to ensure conservation laws while minimizing the introduced bias. In several test cases including Sod's shock tube and Landau damping we show that the proposed method maintains the substantial speed-up of variance reduction method compared to the PIC simulations in the low signal regime with minimal changes to the simulation code.

翻译：我们将最近发展的熵守恒方差缩减框架[M. Sadr, N. G. Hadjiconstantinou, A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction, Journal of Computational Physics 472 (2023) 111677.]扩展至求解Vlasov-Poisson方程的粒子网格法。我们证明，在速度空间推进过程中冻结重要性权重的零阶近似虽然会引入偏差，但具有稳定性。随后，我们基于最大交叉熵原理提出权重分布的修正方法，在保证守恒律的同时最小化引入的偏差。通过Sod激波管和Landau阻尼等多个测试案例，我们证明所提方法在低信噪比条件下，相比传统粒子网格模拟仍能保持方差缩减方法带来的显著加速效果，且对仿真代码的改动极小。