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"
}