2010
DOI: 10.1029/2009wr008792
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Snapshot selection for groundwater model reduction using proper orthogonal decomposition

Abstract: [1] Water resources systems management often requires complex mathematical models whose use may be computationally infeasible for many advanced analyses, e.g., optimization, data assimilation, model uncertainty, etc. The computational demand of these analyses can be reduced by approximating the model with a simpler reduced model. Proper Orthogonal Decomposition (POD) is an efficient model reduction technique based on the projection of the original model onto a subspace generated by full-model snapshots. In ord… Show more

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Cited by 59 publications
(70 citation statements)
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“…POD has been shown to have the ability to reduce the dimension of a groundwater model by several orders of magnitude while maintaining more than 99% accuracy [McPhee and Yeh, 2008]. Siade et al [2010] demonstrated that by applying POD, a groundwater model that originally contained more than 200,000 spatial nodes could be reduced to a model containing only 10 spatial nodes, resulting in an approximately 1000 times increase in speed of solving the model. Note that the temporal dimension remains untouched.…”
Section: Experimental Designmentioning
confidence: 99%
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“…POD has been shown to have the ability to reduce the dimension of a groundwater model by several orders of magnitude while maintaining more than 99% accuracy [McPhee and Yeh, 2008]. Siade et al [2010] demonstrated that by applying POD, a groundwater model that originally contained more than 200,000 spatial nodes could be reduced to a model containing only 10 spatial nodes, resulting in an approximately 1000 times increase in speed of solving the model. Note that the temporal dimension remains untouched.…”
Section: Experimental Designmentioning
confidence: 99%
“…at time t. Equation (6) is referred to as the full model. In most cases of interest matrices, A and B are large, sparse, and positive definite [Siade et al, 2010] (note that, throughout the text, a bold face letter indicates a matrix or vector, whereas a non-bold face letter indicates a scalar. For example, s t indicates the vector of all drawdown values at time t, whereas s t i denotes the drawdown in the ith node at time t).…”
Section: Confined Aquifer Groundwater-flow Modelmentioning
confidence: 99%
“…Let Y 2 R n ´b e the matrix ofś napshots, Y D OEy r 1 ; : : : ; y r´, where r i , i D 1; : : : ;´are the time steps at which the solutions are collected. In the POD approach, the basis vectors are the m eigenvectors corresponding to the m largest eigenvalues of the matrix Y Y T [13,26]. This procedure resembles the Principal Component Analysis and for this reason the basis vectors are also called principal components.…”
Section: Projection-based Reduced Order Modelsmentioning
confidence: 99%
“…To reduce this cost, in many applications, the snapshots are collected only at the beginning of the temporal simulation, for example, as in Vermeulen et al [26], but this approach does not guarantee that the snapshots are representative of the full-model solution for the rest of the simulation. Siade et al [13] proposes an optimal distribution of the snapshots times during the simulation, thus avoiding the computation of the full-system model at each time step. In this work, POD is based on the set of all snapshots evaluated by the full model during the transient simulation over the entire time interval.…”
Section: Snapshot Techniquementioning
confidence: 99%
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