Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models
Name
multi-fidelity-failure-probability-monte-carlo-estimation-peherstorfer-kramer-willcox-TR.pdf
Description
Accepted version
Size
446.69 KB
Format
Adobe PDF
Checksum (MD5)
7346b35a5872be541b6c5b1e76d56621
Author(s)
Peherstorfer, Benjamin
Kramer, Boris
Willcox, Karen
Date Issued
2017
Journal
Journal of Computational Physics
Publisher
Elsevier BV
Citation
Peherstorfer, B., B. Kramer, and K. Willcox. "Combining Multiple Surrogate Models to Accelerate Failure Probability Estimation with Expensive High-Fidelity Models." Journal of Computational Physics 341 (2017): 61-75.
Version
Author's final manuscript
Abstract
© 2017 Elsevier Inc. In failure probability estimation, importance sampling constructs a biasing distribution that targets the failure event such that a small number of model evaluations is sufficient to achieve a Monte Carlo estimate of the failure probability with an acceptable accuracy; however, the construction of the biasing distribution often requires a large number of model evaluations, which can become computationally expensive. We present a mixed multifidelity importance sampling (MMFIS) approach that leverages computationally cheap but erroneous surrogate models for the construction of the biasing distribution and that uses the original high-fidelity model to guarantee unbiased estimates of the failure probability. The key property of our MMFIS estimator is that it can leverage multiple surrogate models for the construction of the biasing distribution, instead of a single surrogate model alone. We show that our MMFIS estimator has a mean-squared error that is up to a constant lower than the mean-squared errors of the corresponding estimators that uses any of the given surrogate models alone—even in settings where no information about the approximation qualities of the surrogate models is available. In particular, our MMFIS approach avoids the problem of selecting the surrogate model that leads to the estimator with the lowest mean-squared error, which is challenging if the approximation quality of the surrogate models is unknown. We demonstrate our MMFIS approach on numerical examples, where we achieve orders of magnitude speedups compared to using the high-fidelity model only.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.JCP.2017.04.012
