Multifidelity Surrogate Modeling for Time-Series Outputs

This paper considers the surrogate modeling of a complex numerical code in a multifidelity frame-work 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.