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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2023, Volume 63, Number 9, Pages 1513–1523
DOI: https://doi.org/10.31857/S0044466923090193 (Mi zvmmf11615) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Optimal control

Numerical algorithm for source determination in a diffusion–logistic model from integral data based on tensor optimization

T. A. Zvonarevaab, S. I. Kabanikhinbc, O. I. Krivorot'koabc

a Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
b Novosibirsk State University, 630090, Novosibirsk, Russia
c Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466923090193
Abstract: An algorithm has been developed for numerically solving the source determination problem in the model of information dissemination in synthetic online social networks, described by reaction–diffusion-type equations, using additional information about the process at fixed time points. The degree of ill-posedness of the source determination problem for a parabolic equation is studied based on the analysis of singular values of the linearized operator of the inverse problem. The algorithm developed is based on a combination of the tensor optimization method and gradient descent supplemented with the A.N.Tikhonov regularization. Numerical calculations demonstrate the smallest relative error in the reconstructed source obtained by the developed algorithm in comparison with classical approaches.
Key words: source determination problem, reaction–diffusion model, inverse problem, tensor optimization, regularization, gradient methods.
Funding agency Grant number
Russian Science Foundation 18-71-10044-П
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-281
This work was supported by the Russian Science Foundation (project no. 18-71-10044-P) and the Mathematical Center in Akademgorodok (agreement with the Ministry of Science and Higher Education of the Russian Federation no. 075-15-2022-281).
Received: 09.12.2022
Revised: 09.12.2022
Accepted: 29.05.2023
English version:
Computational Mathematics and Mathematical Physics, 2023, Volume 63, Issue 9, Pages 1654–1663
DOI: https://doi.org/10.1134/S0965542523090166
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: T. A. Zvonareva, S. I. Kabanikhin, O. I. Krivorot'ko, “Numerical algorithm for source determination in a diffusion–logistic model from integral data based on tensor optimization”, Zh. Vychisl. Mat. Mat. Fiz., 63:9 (2023), 1513–1523; Comput. Math. Math. Phys., 63:9 (2023), 1654–1663
Citation in format AMSBIB
\Bibitem{ZvoKabKri23}
\by T.~A.~Zvonareva, S.~I.~Kabanikhin, O.~I.~Krivorot'ko
\paper Numerical algorithm for source determination in a diffusion--logistic model from integral data based on tensor optimization
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2023
\vol 63
\issue 9
\pages 1513--1523
\mathnet{http://mi.mathnet.ru/zvmmf11615}
\crossref{https://doi.org/10.31857/S0044466923090193}
\elib{https://elibrary.ru/item.asp?id=54313683}
\transl
\jour Comput. Math. Math. Phys.
\yr 2023
\vol 63
\issue 9
\pages 1654--1663
\crossref{https://doi.org/10.1134/S0965542523090166}
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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