# Automatic Differentiation Platform: Design

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 36, Issue: 5, page 783-792
- ISSN: 0764-583X

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topFaure, Christèle. "Automatic Differentiation Platform: Design." ESAIM: Mathematical Modelling and Numerical Analysis 36.5 (2010): 783-792. <http://eudml.org/doc/194126>.

@article{Faure2010,

abstract = {
Automatic differentiation (AD) has proven its interest in many fields of
applied mathematics, but it is still not widely used. Furthermore, existing
numerical methods have been developed under the hypotheses that computing
program derivatives is not affordable for real size problems. Exact derivatives
have therefore been avoided, or replaced by approximations computed by divided
differences. The hypotheses is no longer true due to the maturity of AD added
to the quick evolution of machine capacity. This encourages the development of
new numerical methods that freely make use of program derivatives, and will
require the definition and development of new AD strategies. AD tools must
be extended to produce these new derivative programs, in such a modular way
that the different sub-problems can be solved independently from one another.
Flexibility assures the user to be able to generate whatever specific
derivative program he needs, with at the same time the possibility to generate
standard ones. This paper sketches a new model of modular, extensible and
flexible AD tool that will increase tenfold the DA potential for applied
mathematics. In this model, the AD tool consists of an AD kernel named
KAD supported by a general program transformation platform.
},

author = {Faure, Christèle},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {AD; algorithmic differentiation; computational differentiation;
design; open platform.; automatic differentiation; design; open platform; divided differences},

language = {eng},

month = {3},

number = {5},

pages = {783-792},

publisher = {EDP Sciences},

title = {Automatic Differentiation Platform: Design},

url = {http://eudml.org/doc/194126},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Faure, Christèle

TI - Automatic Differentiation Platform: Design

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 5

SP - 783

EP - 792

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

LA - eng

KW - AD; algorithmic differentiation; computational differentiation;
design; open platform.; automatic differentiation; design; open platform; divided differences

UR - http://eudml.org/doc/194126

ER -

## References

top- M. Berz, C.H. Bischof, G.F. Corliss and A. Griewank, Computational Differentiation: Applications, Techniques, and Tools. SIAM, Philadelphia (1996). Zbl0857.00033
- C. Bischof, A. Carle, P. Khademi, A. Mauer and P. Hovland, Adifor 2.0 User's Guide, Technical Report ANL/MCS-TM-192/CRPC-TR95516-S. Argonne National Laboratory Technical Memorandum and CRPC Technical Report (1998).
- G. Corliss, C. Faure, A. Griewank, L. Hascoet and U. Naumann, Automatic Differentiation: From Simulation to Optimization. Springer-Verlag (2001). Zbl0983.68001
- C. Faure, Adjoining strategies for multi-layered programs. Optim. Methods Softw.17 (2002) 129-164. Zbl1057.68142
- C. Faure and U. Naumann, Minimizing the Tape Size, in Automatic Differentiation: From Simulation to Optimization, G. Corliss, C. Faure, A. Griewank, L. Hascoët and U. Naumann Eds. Springer-Verlag (2001).
- C. Faure and Y. Papegay, Odyssée User's Guide, Version 1.7. Rapport technique 0224. INRIA (1998).
- R. Giering, Tangent linear and Adjoint Model Compiler, Users manual (1997). Unpublished, available from URIhttp://puddle.mit.edu/~ralf/tamc
- R. Giering and T. Kaminski, Generating recomputations in reverse mode, in Automatic Differentiation of Algorithms: From Simulation to Optimization. Springer-Verlag (2001).
- A. Griewank, Principles and Techniques of Algorithmic Differentiation. SIAM (2000). Zbl0958.65028
- A. Griewank and G.F. Corliss, Automatic Differentiation of Algorithms: Theory, Implementation, and Applications. SIAM, Philadelphia (1991). Zbl0747.00030
- Stanford Compiler Group, Suif Compiler System, Technical report. Stanford University.
- M. Iri, Simultaneous computation of functions, partial derivatives and estimates of rounding errors, complexity and practicality. Japan J. Appl. Math.1 (1984) 223-252. Zbl0634.65009
- M. Iri and K. Kubota, Methods of fast automatic differentiation and applications, Research memorandum rmi 87-02, Department of Mathematical Engineering and Instrumentation Physics. Faculty of Engineering, University of Tokyo (1987).
- J. Joss, Algorithmisches Differenzieren. Ph.D. Thesis, ETH Zurich (1976).
- K.V. Kim, Yu.E. Nesterov and B.V. Cherkasskii, An estimate of the effort in computing the gradient. Soviet Math. Dokl.29 (1984) 384-387. Zbl0583.90085
- G.M. Ostrovskii, Yu.M. Volin and W.W. Borisov, Uber die berechnung von ableitungen. Wiss. Z. Tech. Hochsch. Chimie13 (1971) 382-384.
- J.W. Sawyer, First partial differentiation by computer with an application to categorial data analysis. Amer. Statist.38 (1984) 300-308. Zbl0548.65005
- B. Speelpening, Compiling fast partial derivatives of functions given by algorithms. Ph.D. Thesis, University of Illinois, Urbana-Champaign (1980).

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