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Table 1 Mean over the design variables \(\varvec{\vartheta }\) of the “HF-to-MF” models relative error for the objective and constraints when the number of available HF simulations successively equals to 4, 40 and 400 points

From: Constrained multi-fidelity surrogate framework using Bayesian optimization with non-intrusive reduced-order basis

M \(\frac{\varvec{||{\mathcal {J}}-{\mathcal {J}}^{MF}||}}{\varvec{||{\mathcal {J}}||}}\) \(\frac{\varvec{||c_{1}-c_{1}^{MF}||}}{\varvec{||c_{1}||}}\) \(\frac{\varvec{||c_{2}-c_{2}^{MF}||}}{\varvec{||c_{2}||}}\) \(\frac{\varvec{||{\mathcal {J}}-\widetilde{{\mathcal {J}}}||}}{\varvec{||{\mathcal {J}}||}}\) \(\frac{\varvec{||c_{1}-{\widetilde{c}}_{1}||}}{\varvec{||c_{1}||}}\) \(\frac{\varvec{||c_{2}-{\widetilde{c}}_{2}||}}{\varvec{||c_{2}||}}\)
4 6.97% 0.80% 8.10% 8.16% 0.83% 6.59%
40 4.77% 0.59% 7.87 % 4.10% 0.60% 2.34%
400 4.30% 0.61% 4.56 % 0.04% 0.35% 0.11%
  1. The first three columns show the error between the HF model and the MF model without the additive correction. The last three columns show this error after the additive correction of MF model using Gaussian processes