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A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater Flow Models
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 hydraulic conductivity). We use a Karhunen–Loève expansion for a log-normally distributed input field and apply m...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Netherlands
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6390720/ https://www.ncbi.nlm.nih.gov/pubmed/30872876 http://dx.doi.org/10.1007/s11242-018-1065-7 |
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author | Gadd, C. Xing, W. Nezhad, M. Mousavi Shah, A. A. |
author_facet | Gadd, C. Xing, W. Nezhad, M. Mousavi Shah, A. A. |
author_sort | Gadd, C. |
collection | PubMed |
description | 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 hydraulic conductivity). We use a Karhunen–Loève 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 distribution (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. |
format | Online Article Text |
id | pubmed-6390720 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Springer Netherlands |
record_format | MEDLINE/PubMed |
spelling | pubmed-63907202019-03-12 A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater Flow Models Gadd, C. Xing, W. Nezhad, M. Mousavi Shah, A. A. Transp Porous Media Article 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 hydraulic conductivity). We use a Karhunen–Loève 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 distribution (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. Springer Netherlands 2018-05-25 2019 /pmc/articles/PMC6390720/ /pubmed/30872876 http://dx.doi.org/10.1007/s11242-018-1065-7 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
spellingShingle | Article Gadd, C. Xing, W. Nezhad, M. Mousavi Shah, A. A. A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater Flow Models |
title | A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater Flow Models |
title_full | A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater Flow Models |
title_fullStr | A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater Flow Models |
title_full_unstemmed | A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater Flow Models |
title_short | A Surrogate Modelling Approach Based on Nonlinear Dimension Reduction for Uncertainty Quantification in Groundwater Flow Models |
title_sort | surrogate modelling approach based on nonlinear dimension reduction for uncertainty quantification in groundwater flow models |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6390720/ https://www.ncbi.nlm.nih.gov/pubmed/30872876 http://dx.doi.org/10.1007/s11242-018-1065-7 |
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