Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 38. no. 1. P. 54–73. ISSN 2079-6641
INFORMATION AND COMPUTATION TECHNOLOGIES
Some aspects of approximation and interpolation of functions artificial neural networks
V. A. Galkin¹², T. V. Gavrilenko¹², A. D. Smorodinov¹²
¹Surgut Branch of SRISA 628426, Surgut, Energetikov st., 4, Russia
²Surgut State University, 628412, Surgut, Lenina st., 1, Russia
The article deals with the issues of approximation and interpolation of functions f(x) = |x|, f(x) = sin(x), f(x) =1/(1+25x²) with the help of neural networks from those constructed on the basis of the Kolmogorov-Arnold and Tsybenko theorems. problems in training a neural network based on the initialization of weight coefficients in a random way are shown. The possibility of training a neural network to work with a variety is shown.
Keywords: approximation of functions, interpolation of functions, artificial neural networks, Tsybenko’s theorem, Kolmogorov-Arnold’s theorem.
Original article submitted: 22.03.2022
Revision submitted: 04.04.2022
For citation. Galkin V. A., Gavrilenko T. V., Smorodinov A. D. Some aspects of approximation and interpolation of functions artificial neural networks. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 38: 1, 54-73. DOI: 10.26117/2079-6641-2022-38-1-54-73
Competing interests. The author declares that there are no conflicts of interest regarding authorship and publication.
Contribution and Responsibility. The author contributed to this article. The author is solely responsible for providing the final version of the article in print. The author approved the final version of the manuscript.
The content is published under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/deed.ru)
© Galkin V. A., Gavrilenko T. V., Smorodinov A. D., 2022
Funding. The publication was made within the framework of the state task of the Federal State Institution FNTs NIISI RAS (Performance of fundamental scientific research GP 47) on topic No. 0580-2021-0007 «Development of methods for mathematical modeling of distributed systems and corresponding calculation methods».
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Galkin Valery Alekseevich – Doctor of Physical and Mathematical Sciences, Professor, Surgut State University; Director, Branch of SRISA, Surgut, Russia, ORCID 0000-0002-9721-4026.
Gavrilenko Taras Vladimirovich – PhD (Tech.), docent, Surgut State University; Deputy Director, Branch of SRISA, Surgut, Russia, ORCID 0000-0002-3243-2751.
Smorodinov Aleksandr Denisovich – Postgraduate Student of the Department of Applied Mathematics, Lecturer of the Department of ASOIU, Surgut State University»; Engineer of the Department of Biophysics and Neurocybernetics, Branch of SRISA, Surgut, Russia, ORCID 0000-0002-9324-1844.