Sequential design of multi-fidelity computer experiments with effect sparsity

A growing area of focus is using multi-fidelity(MF) simulations to predict the behavior of complex physical systems. In order to adequately utilize the popular sequential designs to improve the effectiveness of the MF method, two challenges involving good projection properties in the presence of effect sparsity and the sample allocation between the high-fidelity(HF) and low-fidelity (LF) codes remain to be addressed. Unfortunately, no systematic study has hitherto been done to deal with these two key issues simultaneously. This article develops a sequential nested design for MF experiments that pays attention to both the space-filling properties in all subsets of factors and the best combination between the two levels of accuracy. For the first issue, we propose a weighted maximum projection criterion combining the uniformity metrics of the HF and LF experiments to select HF points, where the weights are totally data-driven. Note that the obtained HF data is also executed in LF codes to form a nested structure. On the other hand, those samples that only appear in the LF simulation are obtained by the original maximum projection design. The second issue is directly connected with deciding which code to run in the next iteration. We use the entropy theory to score the execution of fidelity for each version, such that the one who has a greater potential to improve the model accuracy will be selected. The performance of the proposed approach is illustrated through several numerical examples. The results demonstrate that the proposed approach outperforms the other three methods in terms of both the prediction accuracy of the final surrogate model and the uniformity in all subspaces of the two codes.