We present a method combining multilevel Monte Carlo (MLMC) and a graph‐based primary subnetwork identification algorithm to provide estimates of the mean and variance of the distribution of first passage times in fracture media at significantly lower computational cost than standard Monte Carlo (MC) methods. Simulations of solute transport are performed using a discrete fracture network (DFN), and instead of using various grid resolutions for levels in the MLMC, which is standard practice in MLMC, we identify a hierarchy of subnetworks in the DFN based on the shortest topological paths through the network using a graph‐based method. While the mean of these ensembles is of critical importance, the variance is also essential in fractured media where uncertainty is an overarching theme, and understanding variability across an ensemble is a requirement for safety assessments. The method provides good estimates of the mean and variance at two orders of magnitude lower computational cost than MC.

中文翻译：

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三维离散断裂网络中首次通过时间的多级蒙特卡洛预测：基于图的方法

我们提出了一种结合多级蒙特卡洛（MLMC）和基于图的主子网识别算法的方法，以比标准蒙特卡洛（MC）低得多的计算成本来提供裂缝介质中首次通过时间分布的均值和方差的估计方法。使用离散断裂网络（DFN）进行溶质运移的模拟，而不是使用MLMC中的各种网格分辨率来作为MLMC中的标准做法，而是使用最短的拓扑路径来确定DFN中子网的层次结构，这是MLMC中的标准做法。通过网络使用基于图的方法。尽管这些合奏的均值至关重要，但在不确定性是首要主题的破裂介质中，差异也是必不可少的，并且了解整个集成的可变性是安全评估的要求。该方法以比MC低两个数量级的计算成本提供了均值和方差的良好估计。