Solving the Laplace Equation by Using Neural Networks

Haffner, Domonkos and Izsák, Ferenc (2021) Solving the Laplace Equation by Using Neural Networks. In: Conference on Developments in Computer Science, Budapest, Hungary, June 17-19, 2021 : Proceedings. Faculty of Informatics, Eötvös Loránd University, Budapest, pp. 1-4.

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Abstract

A neural network approach is presented for solving Laplace equations. The mathematical basis of this approach is the boundary integral method. A shallow and simple neural network is used. The number of the parameters in the neural network is optimal, which results in a quick learning. A numerical experiment is also presented. We can avoid in this way the construction of grids or meshes, which is a significant advance of our approach.

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