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A surrogate modelling approach based on nonlinear dimension reduction for uncertainty quantification in groundwater flow models
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Gadd, Charles W. L., Xing, Wei, Mousavi Nezhad, Mohaddeseh and Shah, Akeel A. (2019) A surrogate modelling approach based on nonlinear dimension reduction for uncertainty quantification in groundwater flow models. Transport in Porous Media, 126 . pp. 39-77. doi:10.1007/s11242-018-1065-7
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Official URL: https://doi.org/10.1007/s11242-018-1065-7
Abstract
In this paper, we develop a surrogate modelling approach for capturing the output field (e.g., the pressure head) from groundwater flow models involving a stochastic input field (e.g., the hy- draulic conductivity). We use a Karhunen-Lo`eve expansion for a log-normally distributed input field, and apply manifold learning (local tangent space alignment) to perform Gaussian process Bayesian inference using Hamiltonian Monte Carlo in an abstract feature space, yielding outputs for arbitrary unseen inputs. We also develop a framework for forward uncertainty quantification in such problems, including analytical approximations of the mean of the marginalized distri- bution (with respect to the inputs). To sample from the distribution we present Monte Carlo approach. Two examples are presented to demonstrate the accuracy of our approach: a Darcy flow model with contaminant transport in 2-d and a Richards equation model in 3-d.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science > Engineering | |||||||||
| Library of Congress Subject Headings (LCSH): | Groundwater flow -- Mathematical models, Stochastic analysis, Bayesian statistical decision theory, Monte Carlo method | |||||||||
| Journal or Publication Title: | Transport in Porous Media | |||||||||
| Publisher: | Springer | |||||||||
| ISSN: | 0169-3913 | |||||||||
| Official Date: | 15 January 2019 | |||||||||
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| Volume: | 126 | |||||||||
| Page Range: | pp. 39-77 | |||||||||
| DOI: | 10.1007/s11242-018-1065-7 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access | |||||||||
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