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
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% |