An adaptive Gaussian process‐based method for efficient Bayesian experimental design in groundwater contaminant source identification problems

Zhang, Jiangjiang; Li, Weixuan; Zeng, Lingzao; Wu, Laosheng

doi:10.1002/2016wr018598

Cited by 114 publications

(72 citation statements)

References 56 publications

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“…Specifically, new parameter points drawn from the approximated posterior distribution by surrogate‐based MCMC are successively added to the existing training dataset, then the GP surrogate is refined locally by conditioning on the new datasets. The coupled approach of surrogate refinement and surrogate‐based MCMC simulation is implemented repeatedly until some predefined criteria are met (Zhang et al, 2016a). The detailed procedure of the adaptive GP‐based MCMC algorithm is: Step 1: Draw N ini design points U = { u 1 , …, u N ini } from the prior distribution to generate the initial training dataset Y = { F ( u 1 ), …, F ( u N ini )}. Step 2: Build the GP surrogate G(⋅) conditioned on the training data Y.…”

Section: Methodsmentioning

confidence: 99%

Efficient Bayesian Inverse Modeling of Water Infiltration in Layered Soils

Gao

Zhang

Liu

et al. 2019

Vadose Zone Journal

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Core Ideas The adaptive GP‐based MCMC was efficient to estimate hydraulic parameters in soils. Accuracy of the estimated parameters was verified by simulating experimental results. These simulations revealed a significant effect of layered structure on soil water flow. Modeling water movement in heterogeneous soils, e.g., layered soils, is an essential but challenging task that requires accurate estimation of multiple sets of soil hydraulic parameters. Markov chain Monte Carlo (MCMC) is a popular but computationally expensive method for parameter estimation. An adaptive Gaussian process (GP)‐based MCMC method proposed in our previous work presents significant computational efficiency. Nevertheless, its performance was evaluated only for synthetic numerical cases and has not been experimentally validated. Furthermore, its applicability in estimating hydraulic parameters of layered soils is still unknown. In this study, we systematically evaluated the performance of the GP‐based MCMC method in estimating the layered soil hydraulic parameters through a water infiltration experiment. It was shown that the proposed method could provide reliable estimations that were very close to those given by the original‐model‐based MCMC but at a much lower computational cost. The simulated soil water dynamics using the estimated parameters revealed a significant effect of layered heterogeneity on water flow. The lower layer(s) with higher water suction may cause persistent unsaturated status of the upper layer(s) during infiltration.

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Section: Methodsmentioning

confidence: 99%

Efficient Bayesian Inverse Modeling of Water Infiltration in Layered Soils

Gao

Zhang

Liu

et al. 2019

Vadose Zone Journal

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“…State‐variable surrogates may outperform log likelihood surrogates when the model state response surface is smoother than that of the log likelihood in parameter space [ Zeng et al ., ]. Generalized polynomial chaos expansion (gPC) [ Marzouk and Xiu , ], sparse grid, and Gaussian process regression methods have been used to construct state‐variable surrogate models in various hydrology applications including groundwater modeling [ Deman et al ., ; Laloy et al ., ; Zeng et al ., ; Zhang et al ., ].…”

Section: Introductionmentioning

confidence: 92%

Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data‐driven error model

Valocchi

et al. 2017

Water Resources Research

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Groundwater model structural error is ubiquitous, due to simplification and/or misrepresentation of real aquifer systems. During model calibration, the basic hydrogeological parameters may be adjusted to compensate for structural error. This may result in biased predictions when such calibrated models are used to forecast aquifer responses to new forcing. We investigate the impact of model structural error on calibration and prediction of a real‐world groundwater flow model, using a Bayesian method with a data‐driven error model to explicitly account for model structural error. The error‐explicit Bayesian method jointly infers model parameters and structural error and thereby reduces parameter compensation. In this study, Bayesian inference is facilitated using high performance computing and fast surrogate models (based on machine learning techniques) as a substitute for the computationally expensive groundwater model. We demonstrate that with explicit treatment of model structural error, the Bayesian method yields parameter posterior distributions that are substantially different from those derived using classical Bayesian calibration that does not account for model structural error. We also found that the error‐explicit Bayesian method gives significantly more accurate prediction along with reasonable credible intervals. Finally, through variance decomposition, we provide a comprehensive assessment of prediction uncertainty contributed from parameter, model structure, and measurement uncertainty. The results suggest that the error‐explicit Bayesian approach provides a solution to real‐world modeling applications for which data support the presence of model structural error, yet model deficiency cannot be specifically identified or corrected.

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“…In most situations, closed‐form expressions of the posterior distribution are nonexistent, so one has to resort to Monte Carlo simulation methods to obtain numerical approximations. Over the past decades, Markov chain Monte Carlo (MCMC) methods have been widely used to assess uncertainties of hydrologic systems conditioned on measurements of observable state variables (Shi et al, ; T. J. Smith & Marshall, ; Vrugt, ; L. Zeng et al, ; X. Zeng et al, ; Zhang et al, ; Zhang et al, ). However, MCMC has to sufficiently explore the parameter space to obtain reliable estimation results.…”

Section: Introductionmentioning

confidence: 99%

Inverse Modeling of Hydrologic Systems with Adaptive Multifidelity Markov Chain Monte Carlo Simulations

Zhang

Man

Lin

et al. 2018

Water Resources Research

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Markov chain Monte Carlo (MCMC) simulation methods are widely used to assess parametric uncertainties of hydrologic models conditioned on measurements of observable state variables. However, when the model is CPU‐intensive and high dimensional, the computational cost of MCMC simulation will be prohibitive. In this situation, a CPU‐efficient while less accurate low‐fidelity model (e.g., a numerical model with a coarser discretization or a data‐driven surrogate) is usually adopted. Nowadays, multifidelity simulation methods that can take advantage of both the efficiency of the low‐fidelity model and the accuracy of the high‐fidelity model are gaining popularity. In the MCMC simulation, as the posterior distribution of the unknown model parameters is the region of interest, it is wise to distribute most of the computational budget (i.e., the high‐fidelity model evaluations) therein. Based on this idea, in this paper we propose an adaptive multifidelity MCMC algorithm for efficient inverse modeling of hydrologic systems. In this method, we evaluate the high‐fidelity model mainly in the posterior region through iteratively running MCMC based on a Gaussian process system that is adaptively constructed with multifidelity simulation. The error of the Gaussian process system is rigorously considered in the MCMC simulation and gradually reduced to a negligible level in the posterior region. Thus, the proposed method can obtain an accurate estimate of the posterior distribution with a small number of the high‐fidelity model evaluations. The performance of the proposed method is demonstrated by three numerical case studies in inverse modeling of hydrologic systems.

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An adaptive Gaussian process‐based method for efficient Bayesian experimental design in groundwater contaminant source identification problems

Cited by 114 publications

References 56 publications

Efficient Bayesian Inverse Modeling of Water Infiltration in Layered Soils

Efficient Bayesian Inverse Modeling of Water Infiltration in Layered Soils

Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data‐driven error model

Inverse Modeling of Hydrologic Systems with Adaptive Multifidelity Markov Chain Monte Carlo Simulations

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