2015
DOI: 10.1007/s00366-015-0397-y
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Performance study of gradient-enhanced Kriging

Abstract: 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… Show more

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Cited by 44 publications
(28 citation statements)
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“…GEK requires only half (or even less) of the training sample points demanded by OK to accurately approximate the actual |S 11 | curve ( Figures 3-5 and Table 1). GEK benefits from the additional gradient data which allow the model to accurately capture the covariance structure of the training data [35,36]. This is achieved by the fact that the GEK model is forced to interpolate both the function and the gradient values at the training samples whereas OK interpolates the function values only.…”
Section: Numerical Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…GEK requires only half (or even less) of the training sample points demanded by OK to accurately approximate the actual |S 11 | curve ( Figures 3-5 and Table 1). GEK benefits from the additional gradient data which allow the model to accurately capture the covariance structure of the training data [35,36]. This is achieved by the fact that the GEK model is forced to interpolate both the function and the gradient values at the training samples whereas OK interpolates the function values only.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…In addition, data of various levels of accuracy can be obtained by executing simulations on various mesh resolutions or with various convergence criteria. Various variable-fidelity metamodeling procedures have been reported in [34][35][36][37].…”
Section: Introductionmentioning
confidence: 99%
“…The simulation code we use was developed by Degroote et al [21]. This code has recently been used as an example problem for Gradient Enhanced Kriging [22] since the function exposes the gradient as well as the objective value. For our purpose, we will ignore the gradients and treat it as a scalar function with vector input consisting of the parameters we want to identify.…”
Section: Artery Simulationmentioning
confidence: 99%
“…Kriging surrogate model is simple and stable compared to other methods and has been widely used in many fields [9][10][11][12]. Some improved Kriging models have 2 Mathematical Problems in Engineering also been studied, such as Gradient-Enhanced Kriging [13], CoKriging [14], and Hierarchical Kriging [15].…”
Section: Introductionmentioning
confidence: 99%