The Wigner Branching Random Walk: Efficient Implementation and Performance Evaluation
The Wigner Branching Random Walk: Efficient Implementation and Performance Evaluation
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DOI：
10.4208/cicp.oa-2018-0141
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发表时间：
2017-09
影响因子：
3.7
通讯作者：
Yunfeng Xiong;Sihong Shao
中科院分区：
文献类型：
--
作者：
Yunfeng Xiong;Sihong Shao
为了实现Wigner分支随机漫步，携带有符号权值（$-1$或$+1$）的粒子比从$-1$到$+1$连续取实值权值的粒子对数据存储和算术操作更友好。前者称为符号粒子，后者称为加权粒子。在本文中，我们提出了两种有效的策略来实现有符号粒子的实现。一是将乘法函数解释为生成粒子对的概率，而不是增量权值；二是利用自举滤波器来调整粒子权值的偏度。对高斯势垒散射（2D）和类氦系统（4D）的性能评估表明了两种方法的可行性和第二种方法的方差缩减特性。我们对第一个签名粒子实现进行了改进，部分减轻了时间步长的限制，并对所有现有的签名粒子实现进行了彻底的理论和数值比较。还提供了根据准概率密度实现重要性采样和有效重采样或粒子缩减的细节。
To implement the Wigner branching random walk, the particle carrying a signed weight, either $-1$ or $+1$, is more friendly to data storage and arithmetic manipulations than that taking a real-valued weight continuously from $-1$ to $+1$. The former is called a signed particle and the latter a weighted particle. In this paper, we propose two efficient strategies to realize the signed-particle implementation. One is to interpret the multiplicative functional as the probability to generate pairs of particles instead of the incremental weight, and the other is to utilize a bootstrap filter to adjust the skewness of particle weights. Performance evaluations on the Gaussian barrier scattering (2D) and a Helium-like system (4D) demonstrate the feasibility of both strategies and the variance reduction property of the second approach. We provide an improvement of the first signed-particle implementation that partially alleviates the restriction on the time step and perform a thorough theoretical and numerical comparison among all the existing signed-particle implementations. Details on implementing the importance sampling according to the quasi-probability density and an efficient resampling or particle reduction are also provided.