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

Research output: Contribution to journalArticlepeer-review

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

Original languageEnglish
Article number113895
Published1 Sep 2021

Bibliographical note

Funding Information: This work was funded as part of the Water Informatics Science and Engineering Centre for Doctoral Training (WISE CDT) under a grant from the Engineering and Physical Sciences Research Council (EPSRC), UK , grant number EP/L016214/1 . TD was funded by a Turing AI Fellowship, UK ( 2TAFFP\100007 ). DM acknowledges support from the EPSRC Platform Grant PRISM, UK ( EP/R029423/1 ). The authors have no competing interests. Data supporting the findings in this study are available in the Open Research Exeter (ORE, ) data repository. Publisher Copyright: © 2021 The Author(s) Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

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Quantifying the uncertainty in model parameters and output is a critical component in model-driven decision support systems for groundwater management. This paper presents a novel algorithmic approach which fuses Markov Chain Monte Carlo (MCMC) and Machine Learning methods to accelerate uncertainty quantification for groundwater flow models. We formulate the governing mathematical model as a Bayesian inverse problem, considering model parameters as a random process with an underlying probability distribution. MCMC allows us to sample from this distribution, but it comes with some limitations: it can be prohibitively expensive when dealing with costly likelihood functions, subsequent samples are often highly correlated, and the standard Metropolis–Hastings algorithm suffers from the curse of dimensionality. This paper designs a Metropolis–Hastings proposal which exploits a deep neural network (DNN) approximation of a groundwater flow model, to significantly accelerate MCMC sampling. We modify a delayed acceptance (DA) model hierarchy, whereby proposals are generated by running short subchains using an inexpensive DNN approximation, resulting in a decorrelation of subsequent fine model proposals. Using a simple adaptive error model, we estimate and correct the bias of the DNN approximation with respect to the posterior distribution on-the-fly. The approach is tested on two synthetic examples; a isotropic two-dimensional problem, and an anisotropic three-dimensional problem. The results show that the cost of uncertainty quantification can be reduced by up to 50% compared to single-level MCMC, depending on the precomputation cost and accuracy of the employed DNN.

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