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• W2471036192 startingPage "1153" @default.
• W2471036192 abstract "An innovative numerical method based on an artificial neural network is presented in order to solve an inverse problem associated with the calculation of the Dirichlet eigenvalues of the anisotropic Laplace operator. Using a set of predefined eigenvalues obtained by solving repeatedly the direct problem, a radial basis neural network is designed with the purpose to find the appropriate components of the anisotropy matrix, related to the Laplace operator, and thus solving the associated inverse problem. The finite element method is used to solve the direct problem and to create the training set for the first radial basis neural network. A nonlinear map of the Dirichlet eigenvalues as a function of the anisotropy matrix is then obtained. This nonlinear relationship is later inverted and refined, by training a second radial basis neural network, solving the aforementioned inverse problem. Some numerical examples are presented to prove the effectiveness of the introduced method." @default.
• W2471036192 created "2016-07-22" @default.
• W2471036192 creator A5011545420 @default.
• W2471036192 creator A5088962074 @default.
• W2471036192 date "2016-08-01" @default.
• W2471036192 modified "2023-10-02" @default.
• W2471036192 title "Neural network solution for an inverse problem associated with the Dirichlet eigenvalues of the anisotropic Laplace operator" @default.
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• W2471036192 doi "https://doi.org/10.1016/j.camwa.2016.06.037" @default.
• W2471036192 hasPublicationYear "2016" @default.
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