Conditional Latin Hypercube Simulation of (Log)Gaussian Random Fields

Liodakis, Stelios; Kyriakidis, Phaedon C.; Gaganis, Petros

doi:10.1007/s11004-017-9715-9

Cited by 8 publications

(2 citation statements)

References 17 publications

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“…Numerical strategies aiming to outperform MCS in terms of computational efficiency include quasi-MC (Caflisch, 1998), multilevel MC (Giles et al, 2015), and various stochastic finite element methods (Xiu, 2010). While widely used in practice, including for subsurface-related applications (e.g., Ciriello et al, 2017;Dodwell et al, 2015;Liodakis et al, 2018; and the references therein), under certain conditions such methods 10.1029/2019WR026090 can be slower than MCS. For example, multilevel MC might become slower than regular MC when estimating a system state's distribution to the same accuracy (Giles et al, 2015), and polynomial chaos-based techniques have been shown to underperform MC if random parameter fields in (nonlinear) models exhibit short correlation lengths and/or high variances (Barajas-Solano & Tartakovsky, 2016).…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Forecast of Single‐Phase Flow in Porous Media With Uncertain Properties

Yang

Boso

Tartakovsky

2019

Water Resources Research

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Uncertainty about geologic makeup and properties of the subsurface renders inadequate a unique quantitative prediction of flow and transport. Instead, multiple alternative scenarios have to be explored within the probabilistic framework, typically by means of Monte Carlo simulations (MCS). These can be computationally expensive, and often prohibitively so, especially when the goal is to compute the tails of a distribution, that is, probabilities of rare events, which are necessary for risk assessment and decision making under uncertainty. We deploy the method of distributions to derive a deterministic equation for the cumulative distribution function (CDF) of hydraulic head in an aquifer with uncertain (random) hydraulic conductivity. The CDF equation relies on a self‐consistent closure approximation, which ensures that the resulting CDF of hydraulic head has the same mean and variance as those computed with statistical moment equations. We conduct a series of numerical experiments dealing with steady‐state two‐dimensional flow driven by either a natural hydraulic head gradient or a pumping well. These experiments reveal that the CDF method remains accurate and robust for highly heterogeneous formations with the variance of log conductivity as large as five. For the same accuracy, it is also up to four orders of magnitude faster than MCS in computing hydraulic head with a required degree of confidence (probability).

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Section: Introductionmentioning

confidence: 99%

Probabilistic Forecast of Single‐Phase Flow in Porous Media With Uncertain Properties

Yang

Boso

Tartakovsky

2019

Water Resources Research

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“…A number of papers have proposed approaches for optimizing the splitting procedure for a spatially distributed trait (Iman and Conover 1982;Stein 1987;Xu et al 2005;May et al 2010;Kyriakidis and Gaganis 2013;Lark and Marchant 2018). In a work by Liodakis et al (2017), the authors compared several stratified Latin hypercube sampling methods (two classical Latin hypercube sampling methods in a conditional simulation context and the stratified likelihood sampling method) and simple random sampling (associated with the Monte Carlo procedure) by means of synthetic hydrogeological case study of flow and transport in a mildly heterogeneous porous medium. The results indicated that the proposed stratified methods were more efficient then simple random sampling.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Splitting of Raw Data into Training and Test Subsets on the Accuracy of Predicting Spatial Distribution by a Multilayer Perceptron

et al. 2019

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The paper discusses the influence of various methods for splitting raw data into test and training subsets on the accuracy of the prediction of the spatial distribution of the variable for the model based on a multilayer perceptron. A comparison of models was performed taking into account both spatial heterogeneity and the spread of values of the modeled variable with a completely random splitting option. The study was based on the results obtained during soil screening of urbanized territories in the Russian subarctic zone, Novy Urengoy city and Noyabrsk city. The spatial distribution of the chemical element chromium (Cr) in the surface layer of the soil was modeled. For both surveyed areas, the models in which a controlled splitting method was used for training demonstrated more accurate results than models trained using completely random splitting.

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The extraction of the training subset for the spatial distribution modelling of the heavy metals in topsoil

Baglaeva

Sergeev

Shichkin

et al. 2021

CATENA

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Conditional Latin Hypercube Simulation of (Log)Gaussian Random Fields

Cited by 8 publications

References 17 publications

Probabilistic Forecast of Single‐Phase Flow in Porous Media With Uncertain Properties

Probabilistic Forecast of Single‐Phase Flow in Porous Media With Uncertain Properties

The Effect of Splitting of Raw Data into Training and Test Subsets on the Accuracy of Predicting Spatial Distribution by a Multilayer Perceptron

The extraction of the training subset for the spatial distribution modelling of the heavy metals in topsoil

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