Publication: Combining Automatic Differentiation Methods for High-Dimensional Nonlinear Models
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Combining Automatic Differentiation Methods for High-Dimensional Nonlinear Models

- incollection -
 

Area
Uncertainty Analysis

Author(s)
James A. Reed , Jean Utke , Hany S. Abdel-Khalik

Published in
Recent Advances in Algorithmic Differentiation

Editor(s)
Shaun Forth, Paul Hovland, Eric Phipps, Jean Utke, Andrea Walther

Year
2012

Publisher
Springer

Abstract
Earlier work has shown that the efficient subspace method can be employed to reduce the effective size of the input data stream for high-dimensional models when the effective rank of the first-order sensitivity matrix is orders of magnitude smaller than the size of the input data. Here, the method is extended to handle nonlinear models, where the evaluation of higher-order derivatives is important but also challenging because the number of derivatives increases exponentially with the size of the input data streams. A recently developed hybrid approach is employed to combine reverse-mode automatic differentiation to calculate first-order derivatives and perform the required reduction in the input data stream, followed by forward-mode automatic differentiation to calculate higher-order derivatives with respect only to the reduced input variables. Three test cases illustrate the viability of the approach.

Cross-References
Forth2012RAi

AD Tools
OpenAD, Rapsodia

AD Theory and Techniques
Higher Order, Reverse Mode

BibTeX
@INCOLLECTION{
         Reed2012CAD,
       title = "Combining Automatic Differentiation Methods for High-Dimensional Nonlinear Models",
       doi = "10.1007/978-3-642-30023-3_3",
       author = "James A. Reed and Jean Utke and Hany S. Abdel-Khalik",
       abstract = "Earlier work has shown that the efficient subspace method can be employed to reduce
         the effective size of the input data stream for high-dimensional models when the effective rank of
         the first-order sensitivity matrix is orders of magnitude smaller than the size of the input data.
         Here, the method is extended to handle nonlinear models, where the evaluation of higher-order
         derivatives is important but also challenging because the number of derivatives increases
         exponentially with the size of the input data streams. A recently developed hybrid approach is
         employed to combine reverse-mode automatic differentiation to calculate first-order derivatives and
         perform the required reduction in the input data stream, followed by forward-mode automatic
         differentiation to calculate higher-order derivatives with respect only to the reduced input
         variables. Three test cases illustrate the viability of the approach.",
       pages = "23--33",
       crossref = "Forth2012RAi",
       booktitle = "Recent Advances in Algorithmic Differentiation",
       series = "Lecture Notes in Computational Science and Engineering",
       publisher = "Springer",
       address = "Berlin",
       volume = "87",
       editor = "Shaun Forth and Paul Hovland and Eric Phipps and Jean Utke and Andrea Walther",
       isbn = "978-3-540-68935-5",
       issn = "1439-7358",
       year = "2012",
       ad_area = "Uncertainty Analysis",
       ad_tools = "OpenAD, Rapsodia",
       ad_theotech = "Higher Order, Reverse Mode"
}


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