Publication: A Hitchhiker's Guide to Automatic Differentiation
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A Hitchhiker's Guide to Automatic Differentiation

- Article in a journal -
 

Author(s)
Philipp H. W. Hoffmann

Published in
Numerical Algorithms

Year
2015

Abstract
This article provides an overview of some of the mathematical principles of Automatic Differentiation (ad). In particular, we summarise different descriptions of the Forward Mode of ad, like the matrix-vector product based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application of the push-forward operator, and explain why they all reduce to the same actual chain of computations.We further give a short mathematical description of some methods of higher-order Forward ad and, at the end of this paper, briefly describe the Reverse Mode of Automatic Differentiation.

AD Theory and Techniques
Introduction

BibTeX
@ARTICLE{
         Hoffmann2015AHG,
       author = "Hoffmann, Philipp H. W.",
       title = "A Hitchhiker's Guide to Automatic Differentiation",
       journal = "Numerical Algorithms",
       year = "2015",
       pages = "1--37",
       abstract = "This article provides an overview of some of the mathematical principles of
         Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward
         Mode of AD, like the matrix-vector product based approach, the idea of lifting functions to the
         algebra of dual numbers, the method of Taylor series expansion on dual numbers and the application
         of the push-forward operator, and explain why they all reduce to the same actual chain of
         computations.We further give a short mathematical description of some methods of higher-order
         Forward AD and, at the end of this paper, briefly describe the Reverse Mode of Automatic
         Differentiation.",
       issn = "1572-9265",
       doi = "10.1007/s11075-015-0067-6",
       url = "http://dx.doi.org/10.1007/s11075-015-0067-6",
       ad_theotech = "Introduction"
}


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