Sensitivity Analysis in the Presence of Intrinsic Stochasticity for Discrete Fracture Network Simulations
arxiv(2023)
摘要
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.
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