Multifidelity Sparse-Grid-Based Uncertainty Quantification for the Hokkaido Nansei-oki Tsunami

Multifidelity Sparse-Grid-Based Uncertainty Quantification for the Hokkaido Nansei-oki Tsunami With uncertainty quantification, we aim to efficiently propagate the uncertainties in the input parameters of a computer simulation, in order to obtain a probability distribution of its output. In this work, we use multi-fidelity sparse grid interpolation to propagate the uncertainty in the shape of the incoming wave for the Okushiri test-case, which is a wave tank model of a part of the 1993 Hokkaido Nansei-oki tsunami. An important issue with many uncertainty quantification approaches is the ‘curse of dimensionality’: the overall computational cost of the uncertainty propagation increases rapidly when we increase the number of uncertain input parameters. We aim to mitigate the curse of dimensionality by using a multifidelity approach. In the multifidelity approach, we combine results from a small number of accurate and expensive high-fidelity simulations with a large number of less accurate but also less expensive low-fidelity simulations. For the Okushiri test-case, we find an improved scaling when we increase the number of uncertain input parameters. This results in a significant reduction of the overall computational cost. For example, for four uncertain input parameters, accurate uncertainty quantification based on only high-fidelity simulations comes at a normalised cost of 219 high-fidelity simulations; when we use a multifidelity approach, this is reduced to a normalised cost of only 10 high-fidelity simulations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Pure and Applied Geophysics Springer Journals

Multifidelity Sparse-Grid-Based Uncertainty Quantification for the Hokkaido Nansei-oki Tsunami

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Earth Sciences; Geophysics/Geodesy
ISSN
0033-4553
eISSN
1420-9136
D.O.I.
10.1007/s00024-017-1606-y
Publisher site
See Article on Publisher Site

Abstract

With uncertainty quantification, we aim to efficiently propagate the uncertainties in the input parameters of a computer simulation, in order to obtain a probability distribution of its output. In this work, we use multi-fidelity sparse grid interpolation to propagate the uncertainty in the shape of the incoming wave for the Okushiri test-case, which is a wave tank model of a part of the 1993 Hokkaido Nansei-oki tsunami. An important issue with many uncertainty quantification approaches is the ‘curse of dimensionality’: the overall computational cost of the uncertainty propagation increases rapidly when we increase the number of uncertain input parameters. We aim to mitigate the curse of dimensionality by using a multifidelity approach. In the multifidelity approach, we combine results from a small number of accurate and expensive high-fidelity simulations with a large number of less accurate but also less expensive low-fidelity simulations. For the Okushiri test-case, we find an improved scaling when we increase the number of uncertain input parameters. This results in a significant reduction of the overall computational cost. For example, for four uncertain input parameters, accurate uncertainty quantification based on only high-fidelity simulations comes at a normalised cost of 219 high-fidelity simulations; when we use a multifidelity approach, this is reduced to a normalised cost of only 10 high-fidelity simulations.

Journal

Pure and Applied GeophysicsSpringer Journals

Published: Jul 18, 2017

References

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