Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion

Laloy, Eric; Rogiers, Bart; Vrugt, Jasper A.; Mallants, Dirk; Jacques, Diederik

doi:10.1002/wrcr.20226

Cited by 234 publications

(161 citation statements)

References 91 publications

(144 reference statements)

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“…The number of variables of each dimensionality reduction, hereafter referred as DR variables, corresponds to the length of the r-vector, r5 r 1 ; r 2 ½ . For the KL transform, the dimensionality reduction variables are the coefficients that multiply the base functions [see e.g., Zhang and Lu, 2004;Li and Cirpka, 2006;Laloy et al, 2013, for details] and we refer to these coefficients as KL variables. -2c and 3a-3c).…”

Section: Effects Of the Dimensionality Reductionmentioning

confidence: 99%

“…A detailed description of this sampling scheme including a proof of ergodicity and detailed balance can be found in the cited references. Various contributions in hydrology and geophysics (amongst others) have demonstrated the ability of DREAM ZS ð Þ to successfully recover high-dimensional target distributions [Laloy et al, , 2013Linde and Vrugt, 2013;RosasCarbajal et al, 2014;Laloy et al, 2014;Lochb€ uhler et al, 2014Lochb€ uhler et al, , 2015.…”

Section: Joint Inference Of Conductivity Fields and Variogram Parametersmentioning

confidence: 99%

“…High-parameter dimensionality poses considerable challenges for the inversion of groundwater flow and transport data [e.g., Kitanidis, 1995;Hendricks-Franssen et al, 2009;Laloy et al, 2013;Zhou et al, 2014, and references therein]. What is more, conceptual and structural inadequacies of the subsurface model and measurement errors of the model input (boundary conditions) and output (calibration) data introduce uncertainty in the estimated parameters and model simulations.…”

Section: Introductionmentioning

confidence: 99%

“…The latter is widely used in subsurface hydrology to represent multi-Gaussian parameter fields. The KL transform uses the covariance function to describe a spatially Gaussian process in a reduced basis [e.g., Zhang and Lu, 2004;Li and Cirpka, 2006;Laloy et al, 2013]. The base functions are the eigenfunctions of the covariance function multiplied by the square root of the associated eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

Laloy

Linde

Jacques

et al. 2015

Water Resources Research

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We present a Bayesian inversion method for the joint inference of high-dimensional multiGaussian hydraulic conductivity fields and associated geostatistical parameters from indirect hydrological data. We combine Gaussian process generation via circulant embedding to decouple the variogram from grid cell specific values, with dimensionality reduction by interpolation to enable Markov chain Monte Carlo (MCMC) simulation. Using the Matern variogram model, this formulation allows inferring the conductivity values simultaneously with the field smoothness (also called Matern shape parameter) and other geostatistical parameters such as the mean, sill, integral scales and anisotropy direction(s) and ratio(s). The proposed dimensionality reduction method systematically honors the underlying variogram and is demonstrated to achieve better performance than the Karhunen-Loè ve expansion. We illustrate our inversion approach using synthetic (error corrupted) data from a tracer experiment in a fairly heterogeneous 10,000-dimensional 2-D conductivity field. A 40-times reduction of the size of the parameter space did not prevent the posterior simulations to appropriately fit the measurement data and the posterior parameter distributions to include the true geostatistical parameter values. Overall, the posterior field realizations covered a wide range of geostatistical models, questioning the common practice of assuming a fixed variogram prior to inference of the hydraulic conductivity values. Our method is shown to be more efficient than sequential Gibbs sampling (SGS) for the considered case study, particularly when implemented on a distributed computing cluster. It is also found to outperform the method of anchored distributions (MAD) for the same computational budget.

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Section: Effects Of the Dimensionality Reductionmentioning

confidence: 99%

Section: Joint Inference Of Conductivity Fields and Variogram Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

Laloy

Linde

Jacques

et al. 2015

Water Resources Research

Self Cite

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“…(a) Data-driven surrogates. These involve empirical approximations of the complex model output calibrated on a set of inputs and outputs of the complex model, for instance neural networks [60], Gaussian processes [31,6], and polynomial chaos expansions [32]. (b) Projection-based methods.…”

Section: Introductionmentioning

confidence: 99%

Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media

Crevillén-García

Wilkinson

Shah

et al. 2017

Advances in Water Resources

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(2017) Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media. Advances in Water Resources, 99 . pp. 1-14. Permanent WRAP URL:http://wrap.warwick.ac.uk/85680 Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. AbstractNumerical groundwater flow and dissolution models of physico-chemical processes in deep aquifers are usually subject to uncertainty in one or more of the model input parameters. This uncertainty is propagated through the equations and needs to be quantified and characterised in order to rely on the model outputs. In this paper we present a Gaussian process emulation method as a tool for performing uncertainty quantification in mathematical models for convection and dissolution processes in porous media. One of the advantages of this method is its ability to significantly reduce the computational cost of an uncertainty analysis, while yielding accurate results, compared to classical Monte Carlo methods. We apply the methodology to a model of convectively-enhanced dissolution processes occurring during carbon capture and storage. In this model, the Gaussian process methodology fails due to the presence of multiple branches of solutions emanating from a bifurcation point, i.e., two equilibrium states exist rather than one. To overcome this issue we use a classifier as a precursor to the Gaussian process emulation, after which we are able to successfully perform a full uncertainty analysis in the vicinity of the bifurcation point.

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Assessment of parametric uncertainty for groundwater reactive transport modeling

Shi

Curtis

et al. 2014

Water Resour. Res.

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The validity of using Gaussian assumptions for model residuals in uncertainty quantification of a groundwater reactive transport model was evaluated in this study. Least squares regression methods explicitly assume Gaussian residuals, and the assumption leads to Gaussian likelihood functions, model parameters, and model predictions. While the Bayesian methods do not explicitly require the Gaussian assumption, Gaussian residuals are widely used. This paper shows that the residuals of the reactive transport model are non-Gaussian, heteroscedastic, and correlated in time; characterizing them requires using a generalized likelihood function such as the formal generalized likelihood function developed by Schoups and Vrugt (2010). For the surface complexation model considered in this study for simulating uranium reactive transport in groundwater, parametric uncertainty is quantified using the least squares regression methods and Bayesian methods with both Gaussian and formal generalized likelihood functions. While the least squares methods and Bayesian methods with Gaussian likelihood function produce similar Gaussian parameter distributions, the parameter distributions of Bayesian uncertainty quantification using the formal generalized likelihood function are non-Gaussian. In addition, predictive performance of formal generalized likelihood function is superior to that of least squares regression and Bayesian methods with Gaussian likelihood function. The Bayesian uncertainty quantification is conducted using the differential evolution adaptive metropolis (DREAM ( zs ) ) algorithm; as a Markov chain Monte Carlo (MCMC) method, it is a robust tool for quantifying uncertainty in groundwater reactive transport models. For the surface complexation model, the regression-based local sensitivity analysis and Morris-and DREAM (ZS) -based global sensitivity analysis yield almost identical ranking of parameter importance. The uncertainty analysis may help select appropriate likelihood functions, improve model calibration, and reduce predictive uncertainty in other groundwater reactive transport and environmental modeling.

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Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion

Cited by 234 publications

References 91 publications

Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media

Assessment of parametric uncertainty for groundwater reactive transport modeling

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