Advanced Experiments on Gaussian Process-based Multi-fidelity Methods over Diverse Mathematical Characteristics

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 Nonlinear-Autoregressive 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.