This paper introduces a new family of hybrid estimators aimed at controlling the efficiency of Monte Carlo computations in particle transport problems. In this context, efficiency is usually measured by the figure of merit (FOM) given by the inverse product of the estimator variance $\mathrm{Var}[\xi ]$ and the run time T: $\mathrm{FOM}:={(\mathrm{Var}[\xi ]T)}^{-1}$. Previously, we developed a new family of transport-constrained unbiased radiance estimators (T-CURE) that generalize the conventional collision and track length estimators [1] and provide 1–2 orders of magnitude additional variance reduction. However, these gains in variance reduction are partly offset by increases in overhead time [2], lowering their computational efficiency. Here we show that combining T-CURE estimation with conventional terminal estimation within each individual biography can moderate the efficiency of the resulting “hybrid” estimator without introducing bias in the computation. This is achieved by treating only the refractive interface crossings with the extended next event estimator, and all others by standard terminal estimators. This is because when there are index-mismatched interfaces between the collision location and the detector, the T-CURE computation rapidly becomes intractable due to the large number of refractions and reflections that can arise. We illustrate the gains in efficiency by comparing our hybrid strategy with more conventional estimation methods in a series of multi-layer numerical examples.

本文介绍了一组新的混合估计器，旨在控制粒子传输问题中蒙特卡洛计算的效率。在这种情况下，效率通常由估计量方差的逆积给出的品质因数 (FOM) 来衡量$\mathrm{变量}[\xi ]$和运行时间T：$\mathrm{FOM}：={(\mathrm{变量}[\xi ]吨)}^{-1}$. 以前，我们开发了一个新的传输约束无偏辐射估计器 (T-CURE) 系列，它概括了传统的碰撞和轨道长度估计器 [1]，并提供了 1-2 个数量级的额外方差减少。然而，这些方差减少的收益部分被开销时间的增加所抵消[2]，从而降低了它们的计算效率。在这里，我们展示了将 T-CURE 估计与传统的终端估计相结合每个人的传记都可以调节所得“混合”估计器的效率，而不会在计算中引入偏差。这是通过仅使用扩展的下一个事件估计器处理折射界面交叉点来实现的，并且通过标准终端估计器处理所有其他的。这是因为当碰撞位置和检测器之间存在折射率不匹配的界面时，由于可能出现大量折射和反射，T-CURE 计算迅速变得难以处理。我们通过在一系列多层数值示例中将我们的混合策略与更传统的估计方法进行比较来说明效率的提高。