Composite Kernel Functions for Surrogate Modeling using Recursive Multi-Fidelity Kriging

In this paper, we propose the use of the composite kernel function (CKL) technique for the multi-fidelity Kriging (MFK) surrogate model. The principle of MFK-CKL is to automatically learn the best combination of single kernels in both low- and high-fidelity Kriging to create a more accurate Kriging model. The combination is in the form of a weighted sum in which the weights are treated as extra hyperparameters. We implement the CKL into the recursive co-Kriging approach. It is relatively straightforward to do the same for other MFK approaches. Demonstrations on a set of non-algebraic problems show the high efficacy of MFK with CKL, outperforming the single kernel approach in terms of approximation error. Besides, the use of CKL successfully eliminates the non-trivial process of manual kernel selection in multi-fidelity Kriging.