We present novel roulette schemes for rare-event sampling that are both structure-preserving and unbiased. The boundaries where Monte Carlo markers are split and deleted are placed automatically and adapted during runtime. Extending existing codes with the new schemes is possible without severe changes because the equation of motion for the markers is not altered. A nonlinear and nonlocal coupling between markers, as in the case of ion cyclotron resonance heating, is permitted. We show results from the ASCOT-RFOF code as an application of the schemes. The amplitude of Monte Carlo noise for 2 MeV ions can be reduced by a factor of 18, what would normally take over 350 times as many markers.

中文翻译：

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蒙特卡罗算法中罕见事件采样的矩保持和网格自适应重加权方法

我们为罕见事件采样提出了新颖的轮盘赌方案，既保持结构又无偏。Monte Carlo 标记被分割和删除的边界在运行时自动放置和调整。由于标记的运动方程没有改变，因此可以在不进行重大更改的情况下使用新方案扩展现有代码。允许标记之间的非线性和非局部耦合，如在离子回旋共振加热的情况下。我们展示了 ASCOT-RFOF 代码的结果作为方案的应用。2 MeV 离子的蒙特卡罗噪声幅度可以降低 18 倍，这通常需要 350 多倍的标记物。