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Performance study of gradient-enhanced Kriging

Selvakumar Ulaganathan (UGent) , Ivo Couckuyt (UGent) , Tom Dhaene (UGent) , Joris Degroote (UGent) and Eric Laermans (UGent)
(2016) ENGINEERING WITH COMPUTERS. 32(1). p.15-34
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Abstract
The use of surrogate models for approximating computationally expensive simulations has been on the rise for the last two decades. Kriging-based 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 stiffness.
Keywords
COMPUTER EXPERIMENTS, IBCN, OPTIMIZATION, DERIVATIVES, ADJOINT, DESIGN, Kriging, Surrogate modelling, Gradient enhancement, Fluid structure interaction

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Citation

Please use this url to cite or link to this publication:

MLA
Ulaganathan, Selvakumar, Ivo Couckuyt, Tom Dhaene, et al. “Performance Study of Gradient-enhanced Kriging.” ENGINEERING WITH COMPUTERS 32.1 (2016): 15–34. Print.
APA
Ulaganathan, S., Couckuyt, I., Dhaene, T., Degroote, J., & Laermans, E. (2016). Performance study of gradient-enhanced Kriging. ENGINEERING WITH COMPUTERS, 32(1), 15–34.
Chicago author-date
Ulaganathan, Selvakumar, Ivo Couckuyt, Tom Dhaene, Joris Degroote, and Eric Laermans. 2016. “Performance Study of Gradient-enhanced Kriging.” Engineering with Computers 32 (1): 15–34.
Chicago author-date (all authors)
Ulaganathan, Selvakumar, Ivo Couckuyt, Tom Dhaene, Joris Degroote, and Eric Laermans. 2016. “Performance Study of Gradient-enhanced Kriging.” Engineering with Computers 32 (1): 15–34.
Vancouver
1.
Ulaganathan S, Couckuyt I, Dhaene T, Degroote J, Laermans E. Performance study of gradient-enhanced Kriging. ENGINEERING WITH COMPUTERS. 2016;32(1):15–34.
IEEE
[1]
S. Ulaganathan, I. Couckuyt, T. Dhaene, J. Degroote, and E. Laermans, “Performance study of gradient-enhanced Kriging,” ENGINEERING WITH COMPUTERS, vol. 32, no. 1, pp. 15–34, 2016.
@article{7237338,
  abstract     = {{The use of surrogate models for approximating computationally expensive simulations has been on the rise for the last two decades. Kriging-based 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 stiffness.}},
  author       = {{Ulaganathan, Selvakumar and Couckuyt, Ivo and Dhaene, Tom and Degroote, Joris and Laermans, Eric}},
  issn         = {{0177-0667}},
  journal      = {{ENGINEERING WITH COMPUTERS}},
  keywords     = {{COMPUTER EXPERIMENTS,IBCN,OPTIMIZATION,DERIVATIVES,ADJOINT,DESIGN,Kriging,Surrogate modelling,Gradient enhancement,Fluid structure interaction}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{15--34}},
  title        = {{Performance study of gradient-enhanced Kriging}},
  url          = {{http://dx.doi.org/10.1007/s00366-015-0397-y}},
  volume       = {{32}},
  year         = {{2016}},
}

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