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| Titel |
Uncertainty quantification for massive autonomous systems based on a second-order adjoint method |
| VerfasserIn |
Shin-ichi Ito, Hiromichi Nagao, Masayuki Kano |
| Konferenz |
EGU General Assembly 2017
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250147424
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| Publikation (Nr.) |
 EGU/EGU2017-11587.pdf |
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| Zusammenfassung |
| Data assimilation (DA) is a fundamental computational technique that integrates numerical
simulation models and observation data based on Bayesian statistics. One key issue is the
implementation of DA in massive simulation models under the constraints of computational
time and resources. We propose a new adjoint-based DA methodology based on the
four-dimensional variation method (4DVar) implemented a second-order adjoint method,
which produces not only optimum estimates but also their uncertainties within the reasonable
computational limitations. The uncertainties are given as diagonal elements of the inverse of
Hessian matrix, which is the covariance matrix of a Gaussian that approximates the
posterior distribution in the neighborhood of the optimum. Conventional algorithms for
deriving the Hessian inverse require O(CN2 + N3) computations and O(N2)
memory, where N is the degree of freedom of a given autonomous system and C is the
number of computations needed to simulate time series of suitable time length. The
proposed method using a second-order adjoint method allows us to directly evaluate the
diagonal elements of the Hessian inverse without computing all of its elements. This
drastically reduces the number of computations to O(C) and the amount of memory
to O(N) for each diagonal element. The proposed method is validated through
numerical tests using a massive two-dimensional Kobayashi phase-field model. We
confirm that the proposed method correctly reproduces the parameter and initial state
assumed in advance, and successfully evaluates the uncertainty of the parameter. |
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