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On the Effectiveness of the Fast Automatic Differentiation Methodology

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Optimization and Applications (OPTIMA 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 974))

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Abstract

In this paper, we compare the three approaches for calculating the gradient of a complex function of many variables. The compared approaches are: the use of precise, analytically derived formulas; the usage of formulas derived with the aid of the Fast Automatic Differentiation methodology; the use of standard software packages that implement the ideas of Fast Automatic Differentiation methodology. Comparison of approaches is carried out with the help of a complex function that represents the energy of atoms system whose interaction potential is the Tersoff potential. As a comparison criterion, the computer time required to calculate the gradient of the function is used. The results show the superiority of the Fast Automatic Differentiation methodology in comparison with the approach using analytical formulas. Standard packages compute the function gradient around the same time as using the formula of the Fast Automatic Differentiation methodology.

This work was partially supported by the Russian Foundation for Basic Research (project no. 17-07-00493 a).

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Authors and Affiliations

  1. Dorodnicyn Computing Centre, Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Moscow, Russia

    Alla Albu, Andrei Gorchakov & Vladimir Zubov

  2. Nuclear Safety Institute of the Russian Academy of Sciences, Moscow, Russia

    Andrei Gorchakov

  3. Moscow Institute of Physics and Technology, Moscow, Russia

    Vladimir Zubov

Authors
  1. Alla Albu
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  2. Andrei Gorchakov
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  3. Vladimir Zubov
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Corresponding author

Correspondence to Vladimir Zubov .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Yury Evtushenko

  2. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  3. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  4. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    Yury Kochetov

  5. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Vlasta Malkova

  6. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Mikhail Posypkin

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Albu, A., Gorchakov, A., Zubov, V. (2019). On the Effectiveness of the Fast Automatic Differentiation Methodology. In: Evtushenko, Y., Jaćimović, M., Khachay, M., Kochetov, Y., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2018. Communications in Computer and Information Science, vol 974. Springer, Cham. https://doi.org/10.1007/978-3-030-10934-9_19

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  • DOI: https://doi.org/10.1007/978-3-030-10934-9_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10933-2

  • Online ISBN: 978-3-030-10934-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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