Accelerating uncertainty quantification of groundwater flow modelling using a deep neural network proxy

Lykkegaard, Mikkel B.; Dodwell, Tim; Moxey, David

doi:10.1016/j.cma.2021.113895

Cited by 13 publications

(9 citation statements)

References 35 publications

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“…Secondly, predicting head changes as distributions instead of single values with a neural network is, to our knowledge, unique to this study. Neural networks have been used to accelerate uncertainty estimates in groundwater modeling (Lykkegaard et al, 2021), but not as direct outputs of the network.…”

Section: Discussionmentioning

confidence: 99%

“…The trained network shows capabilities of mapping hydraulic conductivity fields to corresponding flow simulations with significant time savings as opposed to MODFLOW. Lykkegaard et al (2021) show that the combination of Markov chain Monte Carlo (MCMC) and deep neural networks can reduce the cost of uncertainty quantification for groundwater flow models by up to 50% compared to using a regular Metropolis algorithm. Reductions in computational costs are also mentioned as a great advantage of deep networks (Marais and de Dreuzy, 2017).…”

Section: Introductionmentioning

confidence: 99%

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Hydraulic head change predictions in groundwater models using a probabilistic neural network

Dahl¹,

Vilhelmsen²,

Bach³

et al. 2023

Front. Water

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Groundwater resource management is an increasingly complicated task that is expected to only get harder and more important with future climate change and increasing water demands resulting in an increasing need for fast and accurate decision support systems. Numerical flow simulations are accurate but slow, while response matrix methods are fast but only accurate in near-linear problems. This paper presents a method based on a probabilistic neural network that predicts hydraulic head changes from groundwater abstraction with uncertainty estimates, that is both fast and useful for non-linear problems. A generalized method of constructing and training such a network is demonstrated and applied to a groundwater model case of the San Pedro River Basin. The accuracy and speed of the neural network are compared to results using MODFLOW and a constructed response matrix of the model. The network has fast predictions with results similar to the full numerical solution. The network can adapt to non-linearities in the numerical model that the response matrix method fails at resolving. We discuss the application of the neural network in a decision support framework and describe how the uncertainty estimate accurately describes the uncertainty related to the construction of the training data set.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hydraulic head change predictions in groundwater models using a probabilistic neural network

Dahl¹,

Vilhelmsen²,

Bach³

et al. 2023

Front. Water

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show abstract

“…It has strong approximation ability, classification ability, and learning convergence speed. When the input pattern vector is extended to the hidden layer space, the function set constructs an arbitrary basis, so that the original nonseparable problem in the low dimensional space is transformed into an approximate linear separable problem in the high dimensional space, and the approximation of any function with arbitrary precision is realized [ 50 , 51 , 52 ].…”

Section: Classification Of Evacuation Events Caused By Hcrtasmentioning

confidence: 99%

Hazardous Chemicals Road Transportation Accidents and the Corresponding Evacuation Events from 2012 to 2020 in China: A Review

Zhang

Cheng

Gai

2022

IJERPH

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Based on accident data from the China Chemical Accident Information Network, detailed information was obtained from 2657 hazardous chemicals road transportation accidents (HCRTAs) and 148 evacuations caused by these accidents that occurred in China from 2012 to 2020. The characteristics and the development trend of the present HCRTAs in China and the rate of emergency are obtained via statistical analysis. Based on the probability of evacuation scenarios via historical statistics, the social cost of labor loss value of participating emergency responders, and evacuees’ placement and transfer cost as the consequences of evacuation events, an evacuation event grading model based on social risk assessment is constructed. Evaluating and classifying the risk of evacuation events caused by HCRTAs (148), the results demonstrated that the social risk caused by emergency scenarios F_61 (leakage due to overturning of hazardous chemical vehicles, which led to evacuation) and F_91 (leakage due to rear-end of hazardous chemical vehicles, which led to evacuation) was higher than other emergency scenarios. To reduce the dangers caused by HCRTAs, the framework for improving the emergency response capacity of communities is discussed and analyzed based on five aspects, which comprise land use planning, city construction, education promotion, information construction, and the layout of emergency resources.

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“…Section 4 contains details about the numerical problems to be solved and presents the performance results of the proposed framework on the same problems. One of the numerical problems is SPDE system which governs systems in mechanics such as steady‐state heat conduction, groundwater flow, and other diffusion processes 36‐38 . However, we follow the problem definition similar to Tripathy and Bilionis, 30 where no assumptions are placed on uncertain diffusion's regularity and lengthscale.…”

Section: Introductionmentioning

confidence: 99%

Deep capsule encoder–decoder network for surrogate modeling and uncertainty quantification

Thakur

Chakraborty

2023

Numerical Meth Engineering

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We propose a novel capsule-based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet) architecture into an image-to-image regression encoder-decoder network. Specifically, the aim is to exploit the benefits of CapsNet over convolution neural network (CNN) -retaining pose and position information related to an entity to name a few. The performance of the proposed approach is illustrated by solving two different variants of elliptic partial differential equations (PDE): a stochastic version without a source term having an input dimensionality of 1024 and a deterministic pressure Poisson equation for flow past a cylinder. The first PDE, that is, the stochastic PDE (SPDE), also governs systems in mechanics such as steady heat conduction, groundwater flow, or other diffusion processes. In this article, the problem definition for this SPDE is such that it does not restrict the random diffusion field to a particular covariance structure, and the more strenuous task of response prediction for an arbitrary diffusion field is solved. Finally, we also evaluate the performance of our model on the uncertainty propagation problem based on this equation. The obtained results from the performance evaluation of the developed model on the mentioned problems indicate that the proposed approach is accurate, data efficient, and robust.

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Accelerating uncertainty quantification of groundwater flow modelling using a deep neural network proxy

Cited by 13 publications

References 35 publications

Hydraulic head change predictions in groundwater models using a probabilistic neural network

Hydraulic head change predictions in groundwater models using a probabilistic neural network

Hazardous Chemicals Road Transportation Accidents and the Corresponding Evacuation Events from 2012 to 2020 in China: A Review

Deep capsule encoder–decoder network for surrogate modeling and uncertainty quantification

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