A note on the choice and the estimation of Kriging models for the analysis of deterministic computer experiments

Ginsbourger, David; Dupuy, Delphine; Badea, Anca; Carraro, Laurent; Roustant, Olivier

doi:10.1002/asmb.741

Cited by 30 publications

(18 citation statements)

References 18 publications

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“…1) counterparts irrespective of the conservative second-order di↵erentiability nature as explained in Section 3. For more information on the suitability of various correlation functions in Kriging-based surrogate modelling, the reader is referred to [9][10][11]. Tables 3, 4, 14 (Appendix C) and 15 (Appendix C) give the CVE measure for the benchmark functions and the improvement in surrogate model accuracy reached by the GEK models against the Gaussian correlation function based OK models.…”

Section: Benchmark Test Problemsmentioning

confidence: 99%

Performance study of gradient-enhanced Kriging

Ulaganathan

Couckuyt

Dhaene

et al. 2015

Engineering with Computers

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The use of surrogate models for approximating computationally expensive simulations has been on the rise for the last two decades. Krigingbased surrogate models are popular for approximating deterministic computer models. In this work, the performance of Kriging is investigated when gradient information is introduced for the approximation of computationally expensive black-box simulations. This approach, known as Gradient Enhanced Kriging, is applied to various benchmark functions of varying dimensionality (2D-20D). As expected, results from the benchmark problems show that additional gradient information can significantly enhance the accuracy of Kriging. Gradient Enhanced Kriging provides a better approximation even when gradient information is only partially available. Further comparison between Gradient Enhanced Kriging and an alternative formulation of Gradient Enhanced Kriging, called indirect Gradient Enhanced Kriging, highlights various advantages of directly employing gradient information, such as improved surrogate model accuracy, better conditioning of the correlation matrix, etc. Finally, Gradient Enhanced Kriging is used to model 6-and 10-variable Fluid-Structure Interaction problems from bio-mechanics to identify the arterial wall's sti↵ness.Keywords Kriging · Surrogate Modelling · Gradient Enhancement · Fluid Structure Interaction S. Ulaganathan · I. Couckuyt · T. Dhaene · E. Laermans Ghent University -iMINDS, Department of Information Technology (INTEC), Gaston Crommenlaan 8, 9050 Ghent, Belgium E-mail: {selvakumar.ulaganathan, ivo.couckuyt, tom.dhaene, eric.laermans}@ugent.be J. Degroote Ghent University, Department of Flow, Heat and Combustion Mechanics, Sint -Pietersnieuwstraat 41, 9000 Ghent, Belgium E-mail: Joris.Degroote@ugent.be 2 S e l v a k u m a r U l a g a n a t h a n e t a l .

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Section: Benchmark Test Problemsmentioning

confidence: 99%

Performance study of gradient-enhanced Kriging

Ulaganathan

Couckuyt

Dhaene

et al. 2015

Engineering with Computers

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“…The main difference is with extrapolation (here mainly outside [−1, 1]) where the Kriging mean reverts to the specified trend. For more details, see Ginsbourger, Dupuy, Badea, Carraro, and Roustant (2009).…”

Section: Influence Of the Trendmentioning

confidence: 99%

DiceKriging,DiceOptim: TwoRPackages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization

Roustant¹,

Ginsbourger²,

Deville³

2012

J. Stat. Soft.

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513

471

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We present two recently released R packages, DiceKriging and DiceOptim, for the approximation and the optimization of expensive-to-evaluate deterministic functions. Following a self-contained mini tutorial on Kriging-based approximation and optimization, the functionalities of both packages are detailed and demonstrated in two distinct sections. In particular, the versatility of DiceKriging with respect to trend and noise specifications, covariance parameter estimation, as well as conditional and unconditional simulations are illustrated on the basis of several reproducible numerical experiments. We then put to the fore the implementation of sequential and parallel optimization strategies relying on the expected improvement criterion on the occasion of DiceOptim's presentation. An appendix is dedicated to complementary mathematical and computational details.

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“…Further understanding evolved, and Gaussian process proxy models (Rasmussen & Williams, 2006) are now a familiar tool in many engineering departments. (Forrester & Keane, 2009) (Forrester, 2004) (Forrester, Sobester, & Keane, 2008) (Forrester, Sobester, & Keane, 2007) (Jones, 2001) (Abramson, Audet, & Dennis, 2002) (Booker, et al, 1999) (Rudholm & Wojciechowski, 2007) (Queipo, et al, 2005) (Ginsbourger, Helbert, & Carraro, 2008) (Ginsbourger, Dupuy, Badea, Carraro, & Roustant, 2009) (Jacquet, Truyen, Groen, Lemahieu, & Cornelis, 2005) (Ong, Nair, Keane, & Wong, 2005) (Rougier, 2008) (Williams, Santner, & Notz, 2000) (Wu, Zhang, & Peng, 2010) (Zhou, Ong, Nair, Keane, & Lum, 2007) (Farmer, 2007) (Bliznyuk, et al, 2008;Martin & Simpson, 2005) (Nielsen & Thuesen, 2005) (Morgans, Doolan, & Stephens, 2007).…”

Section: Proxy Models and Optimisationmentioning

confidence: 99%

Bridging the Gap Between Deterministic and Probabilistic Uncertainty Quantification Using Advanced Proxy Based Methods

Goodwin

2015

SPE Reservoir Simulation Symposium

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The use of proxy models for optimisation of expensive functions has demonstrated its value since the 1990's in many industries. Within reservoir engineering, similar techniques have been used for over a decade for history matching, both in commercial tools and in-house software.In addition to efficient history matching, proxy models have a distinct advantage when performing uncertainty quantification of probabilistic forecasts. Markov Chain Monte Carlo (MCMC) methods cannot realistically be applied directly with reservoir simulations, and even fast proxy models can fail dramatically to adequately represent the range of uncertainty if implemented without due care.A pitfall of the use of proxy models is that they are considered 'black box' and their quality is difficult to measure. Engineers prefer to deal with deterministic simulation models which they can evaluate and understand.The main pitfall of simple random walk MCMC techniques, which have begun to appear within reservoir engineering workflows, is a focus on theoretical properties which are not observed in practical implementations. This gives rise to potential gross errors, which are not generally appreciated by practitioners. Advances in recent years within the field of Bayesian statistics have significantly improved this situation, but have not yet been disseminated within the oil and gas industry. This paper describes the limitations of random walk MCMC techniques which are currently used for reservoir prediction studies, and shows how Hamiltonian MCMC techniques, together with an efficient implementation of proxy models, can lead to a more reliable and validated probabilistic uncertainty quantification, whilst also generating a suitable ensemble of deterministic reservoir models. Scientific comparison studies are performed for both an analytical case and a realistic reservoir simulation case to demonstrate the validity of the approach.The benefit of this methodology is to allow asset teams to effectively manage reservoir decisions using a robust and validated understanding of uncertainty. It lays the scientific foundations for the next generation of uncertainty tools and workflows.

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A note on the choice and the estimation of Kriging models for the analysis of deterministic computer experiments

Cited by 30 publications

References 18 publications

Performance study of gradient-enhanced Kriging

Performance study of gradient-enhanced Kriging

DiceKriging,DiceOptim: TwoRPackages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization

Bridging the Gap Between Deterministic and Probabilistic Uncertainty Quantification Using Advanced Proxy Based Methods

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