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

Computational Mathematics and Mathematical Physics volume 57, pages 145–155 (2017)Cite this article

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.

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Authors and Affiliations

  1. Penza State University, Penza, 440026, Russia

    V. I. Gorbachenko & M. V. Zhukov

Authors
  1. V. I. Gorbachenko
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  2. M. V. Zhukov
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Correspondence to V. I. Gorbachenko.

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Original Russian Text © V.I. Gorbachenko, M.V. Zhukov, 2017, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2017, Vol. 57, No. 1, pp. 133–143.

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Gorbachenko, V.I., Zhukov, M.V. Solving boundary value problems of mathematical physics using radial basis function networks. Comput. Math. and Math. Phys. 57, 145–155 (2017). https://doi.org/10.1134/S0965542517010079

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  • DOI: https://doi.org/10.1134/S0965542517010079

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