Geodesic
Evolutionary algorithms of solution to boundary value problems in domains admitting decomposition
Matematičeskoe modelirovanie, Tome 19 (2007) no. 12, pp. 52-62

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Neural networks are considered as an effective and powerful tool for numerical solution of boundary value problems for partial differential equations. In this paper we focus our attention on the case of elliptic equations and domains admitting decomposition. The approximation of Dirichlet problem solution for the Laplace equation in complicated domain by means of neural networks is considered. Some original neural network training algorithms based on ideas of evolution modeling are offered. These algorithms allow some effective parallelization and generalization on similar problems. 
@article{MM_2007_19_12_a5,
     author = {A. N. Vasilyev and D. A. Tarkhov},
     title = {Evolutionary algorithms of solution to boundary value problems in domains admitting decomposition},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {52--62},
     publisher = {mathdoc},
     volume = {19},
     number = {12},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2007_19_12_a5/}
}
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A. N. Vasilyev; D. A. Tarkhov. Evolutionary algorithms of solution to boundary value problems in domains admitting decomposition. Matematičeskoe modelirovanie, Tome 19 (2007) no. 12, pp. 52-62. http://geodesic.mathdoc.fr/item/MM_2007_19_12_a5/