Sensitivity Analysis in the Presence of Intrinsic Stochasticity for Discrete Fracture Network Simulations

• Published in: Journal of geophysical research. Machine learning and computation Vol. 1; no. 3
• Main Authors: Murph, A. C., Strait, J. D., Moran, K. R., Hyman, J. D., Viswanathan, H. S., Stauffer, P. H.
• Format: Journal Article
• Language: English
• Published: United States Wiley 01.09.2024
• Subjects: discrete fracture networks; heteroskedastic Gaussian process; sensitivity analysis; uncertainty quantification
• ISSN: 2993-5210; 2993-5210
• DOI: 10.1029/2023JH000113

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 successfully been used in several engineering applications, estimates of output quantities of interest (QoI) — such as breakthrough time of particles reaching the edge of the system — suffer from two distinct types of uncertainty. A run of a DFN simulator requires several parameters 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 parameters will lead to uncertainty in the QoI, called epistemic uncertainty. Furthermore, since these input settings to DFN simulators control the stochastic processes which 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 (i.e., identical input parameters) 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. Beyond the specific takeaways on which input variables influence uncertainty in the QoI the most, 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. Plain Language Summary Observed heteroskedasticity in Discrete Fracture Network (DFN) simulators, where the “random white noise” changes for different inputs, violates assumptions about constant variance in many traditional regression models. We fit a statistical model on DFN simulation output that directly addresses this issue with the aim of performing a Sensitivity Analysis (SA). In a SA, uncertainty on a Quantity of Interest (QoI)—which for this application is the log‐time until particles simulated through a discrete fracture network reach the surface—is attributed to uncertainty on the DFN simulation input parameters. This analysis leads to a better understanding on which simulation input parameters lead to the greatest variation in the QoI, and how much of the variation on this QoI is noise that cannot be attributed to any input parameters (i.e., white noise). Key Points Discrete fracture network (DFN) simulators where the aleatoric uncertainty changes for different inputs makes several standard statistical methods inadmissible We handle each type of uncertainty separately using heteroskedastic Gaussian Processes from the hetGP package in R The major drivers of variance in the outputs are the input parameters that govern the overall transmissivity of the system