Large‐scale inverse model analyses employing fast randomized data reduction

Surface barriers are commonly installed to reduce downward water movement into contaminated zones. Specifically, evapotranspiration (ET) barriers are used to store water and release it, via ET, before it can percolate into an underlying waste zone. To assess the effectiveness of a surface barrier, we used an existing data set, model‐simulated data, and a dimensionality reduction approach called universal multiple linear regression (uMLR) to optimize the required number of sensors in a 2‐m thick surface barrier. To understand the usefulness of implementing predictive uMLR to accommodate multiple monitoring objectives, we compare several network designs, selected based on down‐sampling of existing data, with a recommended sensor design based on model simulations performed without consideration of existing data. We also added consideration of “fuzzy” design, which allows more practical guidelines for field implementation of uMLR. We found that uMLR, combined with robust decision‐making, provides a simple, flexible, and high‐quality network design for monitoring the total water stored in a surface barrier across multiple uncertain conditions.

Section: Focus and Scopementioning

confidence: 99%

Robust Predictive Design of Field Measurements for Evapotranspiration Barriers Using Universal Multiple linear Regression

Clutter

Ferré

Zhang

et al. 2019

“…Simulating transport in hydrologic systems is critical for numerous applications including groundwater contamination (Cvetkovic et al, 2004;National Research Council, 1996;Neuman, 2005;O'Malley & Vesselinov, 2014a), hydrocarbon extraction (Hyman, Jiménez-Martínez, et al, 2016;Karra et al, 2015), and detection of underground nuclear explosions (Jordan et al, 2014). These applications often demand the use of large-scale models making the simulation of transport computationally demanding (Lichtner et al, 2015), so the use of computationally efficient graph-based models can provide significant benefits to techniques that require a large number of model runs such as model calibration (Lin et al, 2017) or uncertainty quantification (O'Malley & Vesselinov, 2014b).…”

Section: Reduced Order Models Of Dfns: Graph Flow and Transport Predimentioning

confidence: 99%

Advancing Graph‐Based Algorithms for Predicting Flow and Transport in Fractured Rock

Viswanathan

Hyman

Karra

et al. 2018

Self Cite

Discrete fracture network (DFN) models are a powerful alternative to continuum models for subsurface flow and transport simulations because they explicitly include fracture geometry and network topology, thereby allowing for better characterization of the latter's influence on flow and transport through fractured media. Recent advances in high performance computing have opened the door for flow and transport simulations in large explicit three‐dimensional DFN, but this increase in model fidelity and system size comes at a huge computational cost because of the large number of mesh elements required to represent thousands of fractures (with sizes that can range several orders of magnitude, from millimeter to kilometer). In most subsurface applications, fracture characteristics are only known statistically and numerous realizations are needed to bound uncertainty in flow and transport in the system, thereby exacerbating the computational burden. Graphs provide a simple and elegant way to characterize, query, and interrogate fracture network connectivity. We propose a DFN model reduction framework where various graph representations are used in conjunction with high‐fidelity DFN simulations to increase computational efficiency while retaining accuracy of key quantities of interest. The appropriate choice of a graph representation, namely, which attributes of the DFN are to be represented as nodes and which ones as edges connecting those nodes, depends on the relevant scientific questions. We demonstrate that the proposed DFN model reduction framework provides an efficient means for DFN modeling through both system reduction of the DFN using graph‐based properties and combining DFN and graph‐based flow and transport simulations.

“…Lee et al () pointed out that GA can be improved further by using randomized low‐rank matrix approximations to precondition the linear GA update equations. Lin et al () demonstrated, similarly, that the scalability of GA can be substantially improved by using randomized sketching to reduce the effective size of the observation space.…”

Section: Introductionmentioning

confidence: 98%

Randomized Truncated SVD Levenberg‐Marquardt Approach to Geothermal Natural State and History Matching

Bjarkason

Maclaren

O’Sullivan

et al. 2018

The Levenberg‐Marquardt (LM) method is commonly used for inverting models used to describe geothermal, groundwater, or oil and gas reservoirs. In previous studies, LM parameter updates have been made tractable for highly parameterized inverse problems with large data sets by applying matrix factorization methods or iterative linear solvers to approximately solve the update equations. Some studies have shown that basing model updates on the truncated singular value decomposition (TSVD) of a dimensionless sensitivity matrix achieved using Lanczos iteration can speed up the inversion of reservoir models. Lanczos iterations only require the sensitivity matrix times a vector and its transpose times a vector, which are found efficiently using adjoint and direct simulations without the expense of forming a large sensitivity matrix. Nevertheless, Lanczos iteration has the drawback of being a serial process, requiring a separate adjoint solve and direct solve every Lanczos iteration. Randomized methods, developed for low‐rank matrix approximation of large matrices, are more efficient alternatives to the standard Lanczos method. Here we develop LM variants which use randomized methods to find a TSVD of a dimensionless sensitivity matrix when updating parameters. The randomized approach offers improved efficiency by enabling simultaneous solution of all adjoint and direct problems for a parameter update.