This paper considers the surrogate modeling of a complex numerical code in a multifidelity framework when the code output is a time series and two code levels are available: a high-fidelity and expensive code level and a low-fidelity and cheap code level. The goal is to emulate a fast-running approximation of the high-fidelity code level. An original Gaussian process regression method is proposed that uses an experimental design of the low-and high-fidelity code levels. The code output is expanded on a basis built from the experimental design. The first coefficients of the expansion of the code output are processed by a cokriging approach. The last coefficients are processed by a kriging approach with covariance tensorization. The resulting surrogate model provides a predictive mean and a predictive variance of the output of the high-fidelity code level. It is shown to have better performance in terms of prediction errors than standard dimension reduction techniques.
This paper deals with surrogate modeling of a computer code output in a hierarchical multi-fidelity context, i.e., when
the output can be evaluated at different levels of accuracy and computational cost. Using observations of the output at
low- and high-fidelity levels, we propose a method that combines Gaussian process (GP) regression and the Bayesian
neural network (BNN), called the GPBNN method. The low-fidelity output is treated as a single-fidelity code using
classical GP regression. The high-fidelity output is approximated by a BNN that incorporates, in addition to the highfidelity observations, well-chosen realizations of the low-fidelity output emulator. The predictive uncertainty of the final surrogate model is then quantified by a complete characterization of the uncertainties of the different models and their interaction. The GPBNN is compared to most of the multi-fidelity regression methods allowing one to quantify the prediction uncertainty.
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