Journal
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
Volume 58, Issue 2, Pages 399-414Publisher
SPRINGER
DOI: 10.1007/s00158-018-2031-2
Keywords
Bayesian; multi-fidelity; surrogate; scale factor; bumpiness; Gaussian process
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Funding
- U.S. Department of Energy, National Nuclear Security Administration, Advanced Simulation and Computing Program under the Predictive Science Academic Alliance Program [DE-NA0002378]
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This study explores why the use of the low-fidelity scale factor can substantially improve the accuracy of the Bayesian multi-fidelity surrogate (MFS). It is shown analytically that the Bayesian MFS framework utilizes the scale factor to reduce the waviness and variation of the discrepancy function by maximizing the Gaussian process-based likelihood function. Less wavy functions are more accurately fitted, and variation reduction mitigates the effect of fitting error. Bumpiness is another way used to combine waviness and variation. Two examples, Borehole3 and Hartmann6, illustrated that indeed the Bayesian MFS reduced bumpiness using the scale factor. The finding may be useful for MFS using surrogates lacking uncertainty structure, so that likelihood is not an option, but bumpiness may be.
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