Abstract
Groundwater flow models are usually subject to uncertainty as a consequence of the random representation of the conductivity field. In this paper, we use a Gaussian process model based on the simultaneous dimension reduction in the conductivity input and flow field output spaces in order quantify the uncertainty in a model describing the flow of an incompressible liquid in a random heterogeneous porous medium. We show how to significantly reduce the dimensionality of the high-dimensional input and output spaces while retaining the qualitative features of the original model, and secondly how to build a surrogate model for solving the reduced-order stochastic model. A Monte Carlo uncertainty analysis on the full-order model is used for validation of the surrogate model.
Highlights
Groundwater flow models are widely used to study the flow of groundwater and contaminants in soils and aquifers, helping, for example, to mitigate seepage and spillages (Karatzas 2017)
∗ j and uncertainty bounds are computed by using the predictive mean given by a more precise measurement of the accuracy of the Gaussian process (GP) results could be provided by calculating some analytical scores from the numerical data derived in this study, the goal of this application is to show that the GP emulator is able to quantify the uncertainty at the same level of resolution as Monte Carlo (MC), and the results of the GP emulation uncertainty analysis are reported in Fig. 6 by direct comparison of both approaches
We developed a procedure for quantifying the uncertainty introduced by the randomness of the conductivity field on the field output of the groundwater flow model
Summary
Groundwater flow models are widely used to study the flow of groundwater and contaminants in soils and aquifers, helping, for example, to mitigate seepage and spillages (Karatzas 2017). Non-intrusive methods include (generalised) polynomial chaos expansions (Ghanem and Spanos 1991), in which, for instance, the coefficients can be approximated using spectral projection or regression (Xiu and Karniadakis 2002) Such schemes, are limited by the input space dimension and polynomial order and tend to perform poorly with limited observations, especially for highly nonlinear problems (Xiu and Hesthaven 2005; Nobile et al 2008). The original GP modelling framework is impractical for such high-dimensional input and output spaces To overcome this limitation, we use the empirical simultaneous GP model reduction (ESGPMR) method developed in Crevillen-Garcia (2018).
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