In the context of expensive numerical experiments, a promising solution for alleviating the computational costs consists of using partially converged simulations instead of exact solutions. The gain in computational time is at the price of precision in the response. This work addresses the issue of fitting a Gaussian process model to partially converged simulation data for further use in prediction. The main challenge consists of the adequate approximation of the error due to partial convergence, which is correlated in both design variables and time directions. Here, we propose fitting a Gaussian process in the joint space of design parameters and computational time. The model is constructed by building a nonstationary covariance kernel that reflects accurately the actual structure of the error. Practical solutions are proposed for solving parameter estimation issues associated with the proposed model. The method is applied to a computational fluid dynamics test case and shows significant improvement in prediction compared to a classical kriging model.


  1. kriging
  2. computer experiments
  3. covariance kernels

MSC codes

  1. 60G15
  2. 62M20
  3. 62M30

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Information & Authors


Published In

cover image SIAM/ASA Journal on Uncertainty Quantification
SIAM/ASA Journal on Uncertainty Quantification
Pages: 57 - 78
ISSN (online): 2166-2525


Submitted: 29 June 2012
Accepted: 16 January 2013
Published online: 27 March 2013


  1. kriging
  2. computer experiments
  3. covariance kernels

MSC codes

  1. 60G15
  2. 62M20
  3. 62M30



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