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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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