Publication: Efficient Sensitivities for the Spin-up Phase
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Efficient Sensitivities for the Spin-up Phase

- incollection -
 

Area
General

Author(s)
Thomas Kaminski , Ralf Giering , Michael Voßbeck

Published in
Automatic Differentiation: Applications, Theory, and Implementations

Editor(s)
H. M. Bücker, G. Corliss, P. Hovland, U. Naumann, B. Norris

Year
2005

Publisher
Springer

Abstract
In geosciences, it is common to spin up models by integrating with annually repeated boundary conditions. ad-generated code for evaluating sensitivities of the final cyclo-stationary state with respect to model parameters or boundary conditions usually includes a similar iteration for the derivative statements, possibly with a reduced number of iterations. We evaluate an alternative strategy that first carries out the spin-up, then evaluates the full Jacobian for the final iteration and then applies the implicit function theorem to solve for the sensitivities of the cyclo-stationary state. We demonstrate the benefit of the strategy for the spin-up of a simple box-model of the atmospheric transport. We derive a heuristic inequality for this benefit, which increases with the number of iterations and decreases with the size of the state space.

Cross-References
Bucker2005ADA

AD Tools
TAF

AD Theory and Techniques
Iteration

BibTeX
@INCOLLECTION{
         Kaminski2005ESf,
       author = "Thomas Kaminski and Ralf Giering and Michael Vo{\ss}beck",
       title = "Efficient Sensitivities for the Spin-up Phase",
       editor = "H. M. B{\"u}cker and G. Corliss and P. Hovland and U. Naumann and B.
         Norris",
       booktitle = "Automatic Differentiation: {A}pplications, Theory, and Implementations",
       series = "Lecture Notes in Computational Science and Engineering",
       publisher = "Springer",
       year = "2005",
       abstract = "In geosciences, it is common to spin up models by integrating with annually
         repeated boundary conditions. AD-generated code for evaluating sensitivities of the final
         cyclo-stationary state with respect to model parameters or boundary conditions usually includes a
         similar iteration for the derivative statements, possibly with a reduced number of iterations. We
         evaluate an alternative strategy that first carries out the spin-up, then evaluates the full
         Jacobian for the final iteration and then applies the implicit function theorem to solve for the
         sensitivities of the cyclo-stationary state. We demonstrate the benefit of the strategy for the
         spin-up of a simple box-model of the atmospheric transport. We derive a heuristic inequality for
         this benefit, which increases with the number of iterations and decreases with the size of the state
         space.",
       crossref = "Bucker2005ADA",
       ad_tools = "TAF",
       pages = "285--293",
       doi = "10.1007/3-540-28438-9_25",
       ad_area = "General",
       ad_theotech = "Iteration",
       PDF = "http://www.FastOpt.com/papers/kaminskial04b.pdf"
}


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