Performance of multi-fidelity multi-output Kriging for problem with high-dimensional inputs

Recently, multi-fidelity multi-output Kriging have been proposed to take the advantages of both the multi-fidelity and multi-output modelling methods. The predictive performance of multi-fidelity multi-output Kriging model has been evaluated with the modelling efficiency being neglected. In this paper, a multi-fidelity multi-output Kriging model is developed and compared with Kriging, multi-fidelity Kriging, and multi-output Kriging w.r.t. both the modelling accuracy and efficiency. Furthermore, the efficient modelling method for high-dimensional problems is incorporated into the various Kriging models. A 144-dimension engineering problem is established and collected with analytic problems to investigate the modelling accuracy and efficiency. Results show that the multi-output Kriging or multi-fidelity multi-output Kriging model can provide more accurate predictions than the single- or multi-fidelity single-output models on problems with low-dimensional inputs. While, for problems with high-dimensional inputs, the predictive capability of the multi-output Kriging or multi-fidelity multi-output Kriging degenerates significantly with the explosive growth of the time for model construction. With the efficient modelling method, the predictive capability and the modelling efficiency of the multi-output Kriging or multi-fidelity multi-output Kriging model are improved remarkably. However, their performance is still outperformed by single-output multi-fidelity Kriging model throughout the empirical experiments for problems with more than 10 inputs.