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dc.contributor.author
Lüthen, Nora
dc.contributor.author
Marelli, Stefano
dc.contributor.author
Sudret, Bruno
dc.date.accessioned
2021-07-06T04:36:55Z
dc.date.available
2021-07-05T12:55:02Z
dc.date.available
2021-07-06T04:36:55Z
dc.date.issued
2021-06-29
dc.identifier.uri
http://hdl.handle.net/20.500.11850/493099
dc.identifier.doi
10.3929/ethz-b-000493099
dc.description.abstract
The classical uncertainty quantification approach models all uncertainty about a physical process in the form of input uncertainty to a deterministic computational model. However, this is not always possible: sometimes part of the uncertainty such as high-dimensional environmental variables cannot be easily modelled (e.g., earthquakes, wind fields), or there is intrinsic randomness in the model (e.g., epidemiological SIR models). Then the model is a so-called stochastic simulator: even when holding all input parameters at a fixed value, the model response is still a random variable. A stochastic simulator can also be seen as a random field, where the input space acts as its index set. To simulate random fields, a widely used method is Karhunen-Loève expansion (KLE), which represents the random field as an infinite series involving orthonormal deterministic basis functions and a countable number of uncorrelated random variables. However, for inferring a random field from a small set of model evaluations, two challenges have often limited the applicability of KLE [1,2]: the covariance function, which is needed to compute the KLE, is usually not known; and the joint distribution of KL random variables is in general complicated, non-Gaussian and possibly highly dependent, and therefore difficult to model. Our approach addresses these challenges. Building on the success of sparse polynomial chaos expansions (PCE) as surrogate models for deterministic engineering models, we propose to use them to approximate trajectories from the stochastic simulator of interest, which results in a continuous covariance function. After computing the KLE and the KL random variables associated with the trajectories, we infer a parametric form of their joint distribution by using state-of-the-art probabilistic modelling techniques such as vine copulas [3] and generalized lambda distributions [4]. We demonstrate that our approach results in a stochastic emulator with accurate marginals and covariance function, which furthermore can be sampled to obtain new realizations. [1] Poirion, F., & Zentner, I. (2014). Stochastic model construction of observed random phenomena. Probabilistic Engineering Mechanics, 36, 63-71. [2] Azzi, S., Huang, Y., Sudret, B., & Wiart, J. (2019). Surrogate modeling of stochastic functions - application to computational electromagnetic dosimetry. International Journal for Uncertainty Quantification, 9(4). [3] Torre, E., Marelli, S., Embrechts, P., & Sudret, B. (2019). A general framework for data-driven uncertainty quantification under complex input dependencies using vine copulas. Probabilistic Engineering Mechanics, 55, 1-16. [4] Karian, Z. A., & Dudewicz, E. J. (2000). Fitting statistical distributions: the generalized lambda distribution and generalized bootstrap methods. CRC press.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.rights.uri
http://creativecommons.org/licenses/by-nc/4.0/
dc.subject
uncertainty quantification
en_US
dc.subject
surrogate modelling
en_US
dc.subject
Stochastic simulators
en_US
dc.subject
Random fields
en_US
dc.subject
Polynomial chaos expansion (PCE)
en_US
dc.subject
Karhunen-Loève expansion
en_US
dc.title
Surrogating stochastic simulators using Karhunen-Loève expansion, sparse PCE and advanced statistical modelling
en_US
dc.type
Other Conference Item
dc.rights.license
Creative Commons Attribution-NonCommercial 4.0 International
ethz.pages.start
U 18995
en_US
ethz.size
11 p.
en_US
ethz.version.deposit
acceptedVersion
en_US
ethz.event
4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNECOMP 2021)
en_US
ethz.event.location
Athens, Greece
en_US
ethz.event.date
June 28–30, 2021
en_US
ethz.notes
Conference lecture held on June 29, 2021
en_US
ethz.grant
Surrogate Modelling for Stochastic Simulators (SAMOS)
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02115 - Dep. Bau, Umwelt und Geomatik / Dep. of Civil, Env. and Geomatic Eng.::02605 - Institut für Baustatik u. Konstruktion / Institute of Structural Engineering::03962 - Sudret, Bruno / Sudret, Bruno
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02115 - Dep. Bau, Umwelt und Geomatik / Dep. of Civil, Env. and Geomatic Eng.::02605 - Institut für Baustatik u. Konstruktion / Institute of Structural Engineering::03962 - Sudret, Bruno / Sudret, Bruno
en_US
ethz.grant.agreementno
175524
ethz.grant.fundername
SNF
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
Projekte MINT
ethz.date.deposited
2021-07-05T12:55:08Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2021-07-06T04:37:15Z
ethz.rosetta.lastUpdated
2022-03-29T10:17:09Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
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