Title: Adaptive sampling accelerates the hybrid deviational particle simulations Show Chinese title

Title: 自适应采样加速混合偏差粒子模拟

Abstract: To avoid ineffective collisions between the equilibrium states, the hybrid method with deviational particles (HDP) has been proposed to integrate the Fokker-Planck-Landau system, while leaving a new issue in sampling deviational particles from the high-dimensional source term. In this paper, we present an adaptive sampling (AS) strategy that first adaptively reconstructs a piecewise constant approximation of the source term based on sequential clustering via discrepancy estimation, and then samples deviational particles directly from the resulting adaptive piecewise constant function without rejection. The mixture discrepancy, which can be easily calculated thanks to its explicit analytical expression, is employed as a measure of uniformity instead of the star discrepancy the calculation of which is NP-hard. The resulting method, dubbed the HDP-AS method, runs approximately ten times faster than the HDP method while keeping the same accuracy in the Landau damping, two stream instability, bump on tail and Rosenbluth's test problem. Show Chinese abstract

Abstract: 为避免平衡状态之间的无效碰撞，提出了带有偏离粒子的混合方法（HDP）来整合福克-普朗克-兰道系统，但由此在从高维源项中采样偏离粒子方面产生了一个新问题。 在本文中，我们提出了一种自适应采样（AS）策略，该策略首先通过差异估计进行顺序聚类，自适应地重构源项的分段常数近似，然后直接从得到的自适应分段常数函数中采样偏离粒子而无需拒绝。 混合差异由于其显式的解析表达式可以轻松计算，被用作均匀性的度量，而不是计算上NP难的星差异。 所得到的方法被称为HDP-AS方法，在保持兰道阻尼、双流不稳定性、尾部凸起和罗森布卢思测试问题相同精度的情况下，运行速度大约是HDP方法的十倍。