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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 1, Pages 133–143
DOI: https://doi.org/10.7868/S0044466917010082 (Mi zvmmf10513) 		 
This article is cited in 29 scientific papers (total in 29 papers)

Solving boundary value problems of mathematical physics using radial basis function networks

V. I. Gorbachenko, M. V. Zhukov

Penza State University, Penza, Russia
Full-text PDF (786 kB) Citations (29)
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DOI: https://doi.org/10.7868/S0044466917010082
Abstract: A neural network method for solving boundary value problems of mathematical physics is developed. In particular, based on the trust region method, a method for learning radial basis function networks is proposed that significantly reduces the time needed for tuning their parameters. A method for solving coefficient inverse problems that does not require the construction and solution of adjoint problems is proposed.
Key words: boundary value problems of mathematical physics, neural networks, radial basis function networks, learning of neural networks, trust region method, coefficient inverse problems.
Funding agency Grant number
Russian Foundation for Basic Research 16-08-00906_а
14-01-00660_а
14-01-00733_а
Received: 03.02.2016
Revised: 27.06.2016
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 1, Pages 145–155
DOI: https://doi.org/10.1134/S0965542517010079
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: V. I. Gorbachenko, M. V. Zhukov, “Solving boundary value problems of mathematical physics using radial basis function networks”, Zh. Vychisl. Mat. Mat. Fiz., 57:1 (2017), 133–143; Comput. Math. Math. Phys., 57:1 (2017), 145–155
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/zvmmf/v57/i1/p133
    • This publication is cited in the following 29 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    Full-text PDF :164
    References:44
    First page:33
     
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