Adaptivity and uncertainty of multi-fidelity surrogate models for shape optimization
Résumé
This paper studies the estimation of the uncertainty for stochastic RBF multi-fidelity surrogate models, focusing on two issues: limited numbers of data points (which is typical for surrogate models based on numerical simulation results) and noisy data. For the first issue, a default uncertainty is proposed which completes the SRBF estimation. For the second issue, a noise filtering procedure is introduced where the noise is first reduced in the training points, after which the filtered training point data are interpolated. This approach allows to estimate the noise-related uncertainty and the interpolation uncertainty separately. Finally, it is argued that the uncertainty of low-fidelity surrogate models in a multi-fidelity model, should be seen as interpolation uncertainty which is zero in the high-fidelity training points. Tests on analytical functions and data from hydrodynamic shape optimization show that the estimated uncertainties are realistic and can serve as a basis for adaptive sampling procedures, even in the presence of significant noise.
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