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

Abstract

(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.

Deep Convolutional Encoder‐Decoder Networks for Uncertainty Quantification of Dynamic Multiphase Flow in Heterogeneous Media

“…It can then be used as a full replacement of the actual model when performing UQ tasks. Many surrogate methods based on the polynomial chaos expansion (Xiu & Karniadakis, ), Gaussian processes (Rasmussen & Williams, ), and neural networks (Hornik et al, ) have been applied widely to address UQ tasks in groundwater models with random inputs and have shown an impressive approximation accuracy and computational efficiency in comparison to MC methods (Chan & Elsheikh, ; Crevillén‐García et al, ; Li et al, ; Liao & Zhang, ; ; , Liao et al, ; Meng & Li, ; Müller et al, , ; Tian et al, , ).…”

Gaussian process emulators for quantifying uncertainty inCO2spreading predictions in heterogeneous media

“…The most popular approach to building emulators is to use a Gaussian process (GP) (Rasmussen and Williams, 2006), which are equivalent to the kriging models used in geostatistics (Stein, 1999). Gaussian processes describe an infinite collection of random variables, and can be thought of as distributions over functions (Rasmussen and Williams, 2006;Crevillén-García et al, 2017). A GP is fully specified by its mean and covariance functions (Rasmussen and Williams, 2006).…”

“…In our case, direct application of GP would be computationally costly for that a 2, 000 dimensional input space would require thousands of training samples (as the hyperparameters associated with each input component are estimated from the simulator data by solving an optimisation problem, e.g., Crevillén-García et al, 2017). Instead, we can construct a GP emulator by exploiting the spatial structure in Z provided by the exact decomposition of Z on a discrete grid.…”

Multilevel and quasi-Monte Carlo methods for uncertainty quantification in particle travel times through random heterogeneous porous media

“…The circulant embedding method provides fast and exact representations of the Gaussian field but requires the use of the fast Fourier transform method, and thus, it is not straightforward to implement. Two alternatives to the circulant embedding method for producing exact decompositions of the covariance matrix associated to the correlation function given in ( 2.5 ) are the Cholesky method [ 11 , 25 , 26 ] and the KL decomposition [ 22 , 27 ]. These methods are not recommended for covariance functions that are differentiable at zero lag distance, e.g.…”

“…These methods are not recommended for covariance functions that are differentiable at zero lag distance, e.g. the square exponential (or Gaussian) correlation function [ 22 , 28 ]. In those cases, the associated covariance matrix is likely to become extremely ill-conditioned [ 29 , 30 ].…”