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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 1, Pages 61–73
DOI: https://doi.org/10.31857/S0044466923010039 (Mi zvmmf11496) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Optimal control

FAD technique and differentiation of a composite function

A. F. Albua, A. Yu. Gorchakovab, V. I. Zubova

a Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 119333, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466923010039
Abstract: Different approaches to the calculation of the gradient of a composite function of several variables are compared, namely, exact analytically derived formulas, formulas based on the fast automatic differentiation (FAD) technique, and standard software packages implementing the ideas of the FAD technique. The approaches are compared as applied to a composite function representing the energy of a system of atoms with the Tersoff interatomic potential. The comparison criterion is the computer time required for computing the gradient of the function. The results show that the FAD technique is superior to the analytical formulas. The standard packages take nearly the same time to compute the function gradient as the FAD technique formulas.
Key words: fast automatic differentiation, multistep process, standard software packages.
Funding agency Grant number
Russian Science Foundation 21-71-30005
This work was supported in part by the Russian Science Foundation, project no. 21-71-30005.
Received: 27.04.2022
Revised: 27.04.2022
Accepted: 17.09.2022
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 1, Pages 57–68
DOI: https://doi.org/10.1134/S0965542523010037
Bibliographic databases:
Document Type: Article
UDC: 517.23
Language: Russian
Citation: A. F. Albu, A. Yu. Gorchakov, V. I. Zubov, “FAD technique and differentiation of a composite function”, Zh. Vychisl. Mat. Mat. Fiz., 63:1 (2023), 61–73; Comput. Math. Math. Phys., 63:1 (2023), 57–68
Citation in format AMSBIB
\Bibitem{AlbGorZub23}
\by A.~F.~Albu, A.~Yu.~Gorchakov, V.~I.~Zubov
\paper FAD technique and differentiation of a composite function
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 1
\pages 61--73
\mathnet{http://mi.mathnet.ru/zvmmf11496}
\crossref{https://doi.org/10.31857/S0044466923010039}
\elib{https://elibrary.ru/item.asp?id=50404568}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 1
\pages 57--68
\crossref{https://doi.org/10.1134/S0965542523010037}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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