RT Journal Article ID 5e1970130bd779d8 A1 de Baar, Jouke H.S. A1 Dwight, Richard P. A1 Bijl, Hester T1 IMPROVEMENTS TO GRADIENT-ENHANCED KRIGING USING A BAYESIAN INTERPRETATION JF International Journal for Uncertainty Quantification JO IJUQ YR 2014 FD 2014-05-20 VO 4 IS 3 SP 205 OP 223 K1 Gaussian random fields K1 maximum likelihood K1 fluid mechanics AB Cokriging is a flexible tool for constructing surrogate models on the outputs of computer models. It can readily incorporate gradient information, in which form it is named gradient-enhanced Kriging (GEK), and promises accurate surrogate models in >10 dimensions with a moderate number of sample locations for sufficiently smooth responses. However, GEK suffers from several problems: poor robustness and ill-conditionedness of the surface. Furthermore it is unclear how to account for errors in gradients, which are typically larger than errors in values. In this work we derive GEK using Bayes' Theorem, which gives an useful interpretation of the method, allowing construction of a gradient-error contribution. The Bayesian interpretation suggests the "observation error" as a proxy for errors in the output of the computer model. From this point we derive analytic estimates of robustness of the method, which can easily be used to compute upper bounds on the correlation range and lower bounds on the observation error. We thus see that by including the observation error, treatment of errors and robustness go hand in hand. The resulting GEK method is applied to uncertainty quantification for two test problems. PB Begell House LK https://www.dl.begellhouse.com/journals/52034eb04b657aea,348c4184660ca52f,5e1970130bd779d8.html