Multi-Stage Bayesian Surrogate Models (MBSM) are meta-models, constructed using data obtained from different sources, which have the ability to integrate information and responses with different levels of accuracy. In applications of surrogate models for time-dependent systems, the data obtained from physical or computational experiments is usually a sequence of response values over time, measured for different combinations of design parameters. For such applications, the traditional MBSM approach is impractical to incorporate all the observed data in a single model of the system, mainly due to the prohibitive computational effort involved. In this paper, we propose a framework for building surrogate models for time-dependent systems, based on the cokriging technique. The proposed framework regards the observations as a set of time-correlated spatial processes, with a stationary, separable cross-covariance structure of known functional form. Results show that for time-dependent systems, the proposed methodology outperforms joint space-time models built with the traditional MBSM approach both in terms of accuracy and computational effort.

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