期刊
TRANSPORT IN POROUS MEDIA
卷 126, 期 1, 页码 39-77出版社
SPRINGER
DOI: 10.1007/s11242-018-1065-7
关键词
Groundwater flow models; Uncertainty quantification; Surrogate model; Karhunen-Loeve expansion; Manifold learning
资金
- EPSRC, UK [EP/P012620/1]
- EPSRC [EP/P012620/1] Funding Source: UKRI
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-Loeve 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.
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