Heterogeneity and a paucity of measurements of key material properties undermine the veracity of quantitative predictions of subsurface flow and transport. For such model forecasts to be useful as a management tool, they must be accompanied by computationally expensive uncertainty quantification, which yields confidence intervals, probability of exceedance, and so forth. We design and implement novel multilevel Monte Carlo (MLMC) algorithms that accelerate estimation of the cumulative distribution functions (CDFs) of quantities of interest, for example, water breakthrough time or oil production rate. Compared to standard non‐smoothed MLMC, the new estimators achieve a significant variance reduction at each discretization level by smoothing the indicator function with a Gaussian kernel or replacing standard Monte Carlo (MC) with the recently developed hierarchical Latinized stratified sampling (HLSS). After validating the kernel‐smoothed MLMC and HLSS‐enhanced MLMC methods on a single‐phase flow test bed, we demonstrate that they are orders of magnitude faster than standard MC for estimating the CDF of breakthrough times in multiphase flow problems.

中文翻译：

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基于内核的平滑和拉丁化分层加速多层蒙特卡洛

异质性和关键材料性能的测量不足，破坏了地下流动和运移定量预测的准确性。为了使此类模型预测可用作管理工具，必须伴随着计算量大的不确定性量化，这会产生置信区间，超出概率等。我们设计并实现了新颖的多级蒙特卡洛（MLMC）算法，该算法可加快对感兴趣的数量（例如水突破时间或产油率）的累积分布函数（CDF）的估计。与标准的非平滑MLMC相比，通过使用高斯核对指标函数进行平滑处理，或使用最近开发的分层分层分层抽样（HLSS）代替标准的蒙特卡洛（MC），新的估算器可在每个离散化级别上显着降低方差。在单相流动试验台上验证了内核平滑的MLMC和HLSS增强的MLMC方法后，我们证明了它们在估算多相流动问题中突破时间的CDF方面比标准MC快几个数量级。