8th European Congress on Computational Methods in Applied Sciences and Engineering, Oslo, Norveç, 5 - 09 Haziran 2022, ss.1-12
Advanced applications of multi-fidelity surrogate modelling techniques provide significant improvements in optimization and uncertainty quantification studies in many engineering fields. Multi-fidelity surrogate modelling can efficiently save the design process from the
computational time burden caused by the need for numerous computationally expensive simulations. However, no consensus exists about which multi-fidelity surrogate modelling technique
usually exhibits superiority over the other methods given for certain conditions. Therefore, the
present paper focuses on assessing the performances of the Gaussian Process-based multi-fidelity
methods across selected benchmark problems, especially chosen to capture diverse mathematical
characteristics, by experimenting with their learning processes concerning different performance
criteria. In this study, a comparison of Linear-Autoregressive Gaussian Process and NonlinearAutoregressive Gaussian Process methods is presented by using benchmark problems that mimic
the behaviour of real engineering problems such as localized behaviours, multi-modality, noise,
discontinuous response, and different discrepancy types. Our results indicate that the considered methodologies were able to capture the behaviour of the actual function sufficiently within
the limited amount of budget for 1-D cases. As the problem dimension increases, the required
number of training data increases exponentially to construct an acceptable surrogate model. Especially in higher dimensions, i.e. more than 5-D, local error metrics reveal that more training
data is needed to attain an efficient surrogate for Gaussian Process based strategies.