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Engineering with Computers

, Volume 32, Issue 1, pp 15–34 | Cite as

Performance study of gradient-enhanced Kriging

  • Selvakumar Ulaganathan
  • Ivo Couckuyt
  • Tom Dhaene
  • Joris Degroote
  • Eric Laermans
Original Article

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

Kriging Surrogate modelling Gradient enhancement Fluid structure interaction 

Notes

Acknowledgments

This research has been funded by the Interuniversity Attraction Poles Programme BESTCOM initiated by the Belgian Science Policy Office. Additionally, this research has been supported by the Fund for Scientific Research in Flanders (FWO-Vlaanderen). Ivo Couckuyt and Joris Degroote are post-doctoral research fellows of the Research Foundation Flanders (FWO).

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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Selvakumar Ulaganathan
    • 1
  • Ivo Couckuyt
    • 1
  • Tom Dhaene
    • 1
  • Joris Degroote
    • 2
  • Eric Laermans
    • 1
  1. 1.Department of Information Technology (INTEC)Ghent University-iMINDSGhentBelgium
  2. 2.Department of Flow, Heat and Combustion MechanicsGhent UniversityGhentBelgium

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