Geodesic
Solving boundary value problems of mathematical physics using radial basis function networks
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 1, pp. 133-143

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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. 
@article{ZVMMF_2017_57_1_a11,
     author = {V. I. Gorbachenko and M. V. Zhukov},
     title = {Solving boundary value problems of mathematical physics using radial basis function networks},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {133--143},
     publisher = {mathdoc},
     volume = {57},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_1_a11/}
}
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V. I. Gorbachenko; M. V. Zhukov. Solving boundary value problems of mathematical physics using radial basis function networks. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 1, pp. 133-143. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_1_a11/