Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion

By Eric Laloy, B. Rogiers, Jasper A. Vrugt, Dirk Mallants, Diederik Jacques. 2013

256 citations recorded by the source corpus.

Subfields: Environmental Engineering, Geophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/068e81b35b191bdc0c659db76231103d9c1858a7

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In Environmental Engineering

In Geophysics

Citations in the corpus

Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method (2014, background): “Several studies (Huang, 2001; Laloy et al., 2013) took the ratio of the expected energy, ε, as a measure of the accuracy of the truncated series, which is defined as ε ¼ Z Ω E eHi x; yð Þ−μ i 2dxdy= Z Ω E Hi x; yð Þ−μ ið Þ 2 dxdy ¼ Xn i¼1 λi= X∞ i¼1 λi ð5Þ where the eigenvalues λi are sorted in a…”
Deep Convolutional Encoder‐Decoder Networks for Uncertainty Quantification of Dynamic Multiphase Flow in Heterogeneous Media (2018, methodology): “One then constructs a surrogate model from this latent space to the model outputs [ Laloy et al. , 2013; Li et al. , 2009; Liao and Zhang , 2013, 2014, 2016; Liao et al. , 2017; Lin and Tartakovsky , 2009; Meng and Li , 2017; M¨uller et al. , 2011].”
Training‐Image Based Geostatistical Inversion Using a Spatial Generative Adversarial Neural Network (2017, background): “Various studies in hydrology and geophysics (amongst others) have shown that DREAM (ZS) can derive posterior distributions with 25-250 dimensions (e.g., Laloy et al. , 2012, 2013; Linde and Vrugt , 2013; Laloy et al. , 2015; Lochbühler et al. , 2015).”
Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions (2014, background): “…of the complex model inputs into the outputs, namely objective functions and/or constraints (Bieker et al., 2007; Blanning, 1975; Broad et al., 2005, 2010; Gorissen et al., 2010; Keating et al., 2010; Kleijnen, 2009; Laloy et al., 2013; Queipo et al., 2005; Yan and Minsker, 2006, 2011).”
Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates (2014, background): “However, the presented test cases in [25] were limited to steady state models.”
Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods (2016, methodology): “This is feasible, given that surrogate modeling has been widely used in uncertainty quantification of groundwater modeling [Razavi et al., 2012; Laloy et al., 2013; Zhang et al., 2013].”
Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations (2015, background): “Reference Objective of PCE application Type of problem Number/name of uncertain inputs Uncertain output(s) Type of polynomial Order of PCE(s) Method for selection of data points Method for the estimation of PCE coefficients Li and Zhang (2007) UP Flow in saturated media (1D, 2D/HE) 6, 7/hydraulic co”
Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation (2016, background): “Benchmark experiments in geophysics, hydrology and hydrogeology have shown that this sampler1200 is able to sample correctly high-dimensional target distributions (Laloy and Vrugt, 2012a; Laloy et al., 2012b, 2013; Linde and Vrugt, 2013;1202 Carbajal et al., 2014; Lochbühler et al., 2014, 2015).”
Assessment of parametric uncertainty for groundwater reactive transport modeling (2014, methodology): “The computational cost of DREAM(ZS) may be reduced by using computationally efficient surrogate models [Razavi et al., 2012], which have be implemented using polynomial chaos expansion [Laloy et al., 2013] and sparse grid collocation [Zhang et al., 2013] within the DREAM framework.”