BibTeX
@INCOLLECTION{
Reed2012CAD,
title = "Combining Automatic Differentiation Methods for HighDimensional Nonlinear Models",
doi = "10.1007/9783642300233_3",
author = "James A. Reed and Jean Utke and Hany S. AbdelKhalik",
abstract = "Earlier work has shown that the efficient subspace method can be employed to reduce
the effective size of the input data stream for highdimensional models when the effective rank of
the firstorder 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 higherorder
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 reversemode automatic differentiation to calculate firstorder derivatives and
perform the required reduction in the input data stream, followed by forwardmode automatic
differentiation to calculate higherorder derivatives with respect only to the reduced input
variables. Three test cases illustrate the viability of the approach.",
pages = "2333",
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 = "9783540689355",
issn = "14397358",
year = "2012",
ad_area = "Uncertainty Analysis",
ad_tools = "OpenAD, Rapsodia",
ad_theotech = "Higher Order, Reverse Mode"
}
