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Automatic Differentiation Platform: Design

Published online by Cambridge University Press:  15 October 2002

Christèle Faure
Christèle Faure*
Affiliation:
PolySpace Technologies, 28 rue Estienne d'Orves, 92120 Montrouge, France. [email protected].
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Abstract

Automatic differentiation (AD) has proven its interest in many fields ofapplied mathematics, but it is still not widely used. Furthermore, existingnumerical methods have been developed under the hypotheses that computingprogram derivatives is not affordable for real size problems. Exact derivativeshave therefore been avoided, or replaced by approximations computed by divideddifferences. The hypotheses is no longer true due to the maturity of AD addedto the quick evolution of machine capacity. This encourages the development ofnew numerical methods that freely make use of program derivatives, and willrequire the definition and development of new AD strategies. AD tools mustbe extended to produce these new derivative programs, in such a modular waythat the different sub-problems can be solved independently from one another.Flexibility assures the user to be able to generate whatever specificderivative program he needs, with at the same time the possibility to generatestandard ones. This paper sketches a new model of modular, extensible andflexible AD tool that will increase tenfold the DA potential for appliedmathematics. In this model, the AD tool consists of an AD kernel namedKAD supported by a general program transformation platform.

Keywords

ADalgorithmic differentiationcomputational differentiationdesignopen platform.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 5: Special issue on Programming , September 2002 , pp. 783 - 792
Copyright
© EDP Sciences, SMAI, 2002

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