Large-scale discrete fracture network (DFN) simulators are standard fare for studies involving the sub-surface transport of particles since direct observation of real world underground fracture networks is generally infeasible. While these simulators have seen numerous successes over several engineering applications, estimations on quantities of interest (QoI) - such as breakthrough time of particles reaching the edge of the system - suffer from a two distinct types of uncertainty. A run of a DFN simulator requires several parameter values to be set that dictate the placement and size of fractures, the density of fractures, and the overall permeability of the system; uncertainty on the proper parameter choices will lead to some amount of uncertainty in the QoI, called epistemic uncertainty. Furthermore, since DFN simulators rely on stochastic processes to place fractures and govern flow, understanding how this randomness affects the QoI requires several runs of the simulator at distinct random seeds. The uncertainty in the QoI attributed to different realizations (i.e. different seeds) of the same random process leads to a second type of uncertainty, called aleatoric uncertainty. In this paper, we perform a Sensitivity Analysis, which directly attributes the uncertainty observed in the QoI to the epistemic uncertainty from each input parameter and to the aleatoric uncertainty. We make several design choices to handle an observed heteroskedasticity in DFN simulators, where the aleatoric uncertainty changes for different inputs, since the quality makes several standard statistical methods inadmissible. Beyond the specific takeaways on which input variables affect uncertainty the most for DFN simulators, a major contribution of this paper is the introduction of a statistically rigorous workflow for characterizing the uncertainty in DFN flow simulations that exhibit heteroskedasticity.

翻译：大规模离散裂缝网络（DFN）模拟器是研究地下颗粒输运的标准工具，因为直接观测真实世界地下裂缝网络通常不可行。尽管这些模拟器在多个工程应用中取得了诸多成功，但对关注量（QoI，如粒子到达系统边界的突破时间）的估计仍受两种不同类型不确定性的影响。运行DFN模拟器需设置多个参数值，这些参数决定了裂缝的位置、尺寸、密度及系统的整体渗透性；参数选择不当将导致QoI产生一定量的不确定性，即认知不确定性。此外，由于DFN模拟器依赖随机过程来布置裂缝并控制流动，理解这种随机性对QoI的影响需要在不同随机种子下多次运行模拟器。由同一随机过程的不同实现（即不同种子）引起的QoI不确定性属于第二种类型，即偶然不确定性。本文通过灵敏度分析，将QoI中观测到的不确定性直接归因于每个输入参数的认知不确定性及偶然不确定性。我们采取多项设计策略来处理DFN模拟器中观测到的异方差性——即不同输入下偶然不确定性发生变化的情况，因为该特性使得若干标准统计方法不再适用。除阐明DFN模拟器中哪些输入变量对不确定性影响最大这一具体结论外，本文的主要贡献在于引入了一套具有统计严谨性的工作流程，用于表征存在异方差性的DFN流动模拟中的不确定性。