A proposed Fast algorithm to construct the system matrices for a reduced-order groundwater model

Ushijima, Timothy T.; Yeh, William W.‐G.

doi:10.1016/j.advwatres.2017.01.010

Cited by 5 publications

(2 citation statements)

References 37 publications

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“…However, as a result of simplification, this approach has the potential to produce significant errors, or deviations, from the complex model. Although there are newly emerging projection-based techniques for producing extremely accurate low-fidelity models, such as proper orthogonal decomposition (Gosses et al, 2018;Ushijima & Yeh, 2017;Siade et al, 2010Siade et al, , 2012 and dynamic mode decomposition (Schmid, 2010), these methods are mainly limited to linear, well-behaved models and likely infeasible for real-world models involving complex, nonlinear, discontinuous boundary conditions and processes. The second, data-driven, category aims to develop some kind of empirical surrogate model that approximates the input-output relationships of the complex model.…”

Section: 1029/2019wr026061mentioning

confidence: 99%

Reduced‐Dimensional Gaussian Process Machine Learning for Groundwater Allocation Planning Using Swarm Theory

Siade

Cui

Karelse³

et al. 2020

Water Resources Research

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Groundwater management and allocation planning involves a rigorous assessment of the performance of operational decisions such as extraction/injection rates on community and environmental objectives. Maximizing performance through numerical optimization can be essential for high‐value resources and is often computationally infeasible due to long simulation model run times combined with nonconvex objectives and constraints. In order to mitigate these drawbacks, surrogate models can be used in place of complex models during the optimization process. There exist a number of machine learning techniques that can be used to develop a data‐driven surrogate model. However, the curse of dimensionality, common to groundwater management, limits the use of these techniques due to the necessity for large training data sets. Even though it is now possible to handle large data sets, the generation of these data sets themselves remains computationally prohibitive as they require numerous simulations to produce accurate surrogates. In this study, we integrate a dimensionality reduction method using truncated singular value decomposition to reduce the number of decision variables, thereby reducing the size of the training data set needed. Correspondingly, we demonstrate a simple technique for acquiring an approximate minimax Latin Hypercube design from within the subspace. We also implement a novel technique for adaptive resampling through particle swarm optimization in order to maintain accuracy of the surrogate model throughout the optimization process. The resulting accurate surrogate model for the Perth regional aquifer system of Western Australia runs in a matter of seconds. Adopting this approach can produce timely solutions, making formal optimization tractable for practitioners.

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Section: 1029/2019wr026061mentioning

confidence: 99%

Reduced‐Dimensional Gaussian Process Machine Learning for Groundwater Allocation Planning Using Swarm Theory

Siade

Cui

Karelse³

et al. 2020

Water Resources Research

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“…In such cases, application of alternative methods such as reduced-order models (ROMs) based on proper orthogonal decomposition (POD) may be an alternative (Esfahanian and Ashrafi, 2009). The accuracy of ROMs has been shown to be compatible with GQSMs while ROMs pose a much simpler structure (Cardoso et al, 2009;Ushijima and Yeh, 2017). In ROMs based on eigenvectors the dominant spatiotemporal modes of the target are calculated.…”

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confidence: 99%

A novel model for simulation of nitrate in aquifers

Noori

Dodangeh

Berndtsson

et al. 2018

Preprint

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Abstract. Please Numerical groundwater quality models (GQMs) often run at high computational cost resulting in long simulation times and complex parameter calibration that limit their practical applications. In this study, a novel reduced-order model (ROM) was developed for nitrate simulation in groundwater including a simple structure and with similar accuracy as more extensive GQMs. The proposed methodology for the development of ROM presents a solution for the problem in ROMs developed with eigenvectors, to make predictions into the future. The model performance was investigated by simulation of nitrate in the Karaj Aquifer, Iran. The dominant modes of spatiotemporal variation of nitrate during a five-year period was calculated by the model. The results revealed an excellent agreement between nitrate simulated by the ROM and the well-known Modular Transport 3D Multi Species (MT3DMS). The absolute error between the ROM and the MT3DMS was less than 0.5 mg/l in the most parts of the aquifer. Thus, results confirm that the use of ROM has advantages through a much simpler structure and shorter calculation times. Observed spatiotemporal variation of nitrate in the aquifer was well represented by the ROM simulations. The simplicity of the model makes it highly interesting also to other water resources problems.

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PODMT3DMS-Tool: proper orthogonal decomposition linked to the MT3DMS model for nitrate simulation in aquifers

et al. 2020

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A proposed Fast algorithm to construct the system matrices for a reduced-order groundwater model

Cited by 5 publications

References 37 publications

Reduced‐Dimensional Gaussian Process Machine Learning for Groundwater Allocation Planning Using Swarm Theory

Reduced‐Dimensional Gaussian Process Machine Learning for Groundwater Allocation Planning Using Swarm Theory

A novel model for simulation of nitrate in aquifers

PODMT3DMS-Tool: proper orthogonal decomposition linked to the MT3DMS model for nitrate simulation in aquifers

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