Leveraging the nugget parameter for efficient Gaussian process modeling

Ramin Bostanabad, Tucker Kearney, Siyu Tao, Daniel W. Apley, Wei Chen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


Gaussian process (GP) metamodels have been widely used as surrogates for computer simulations or physical experiments. The heart of GP modeling lies in optimizing the log-likelihood function with respect to the hyperparameters to fit the model to a set of observations. The complexity of the log-likelihood function, computational expense, and numerical instabilities challenge this process. These issues limit the applicability of GP models more when the size of the training data set and/or problem dimensionality increase. To address these issues, we develop a novel approach for fitting GP models that significantly improves computational expense and prediction accuracy. Our approach leverages the smoothing effect of the nugget parameter on the log-likelihood profile to track the evolution of the optimal hyperparameter estimates as the nugget parameter is adaptively varied. The new approach is implemented in the R package GPM and compared to a popular GP modeling R package (GPfit) for a set of benchmark problems. The effectiveness of the approach is also demonstrated using an engineering problem to learn the constitutive law of a hyperelastic composite where the required level of accuracy in estimating the response gradient necessitates a large training data set.

Original languageEnglish (US)
Pages (from-to)501-516
Number of pages16
JournalInternational Journal for Numerical Methods in Engineering
Issue number5
StatePublished - May 4 2018


  • Gaussian process
  • computer experiments
  • hyperparameter estimation
  • ill-conditioned matrix
  • nugget parameter

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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