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ReLU Neural Network Galerkin BEM

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Bibliographic Details
Main Authors: Rubén, Aylwin, Fernando, Henríquez, Christoph, Schwab
Format: Book
Language:English
Published: Springer 2023
Subjects:
ReLU-NNs
Galerkin discretization
Online Access:https://link.springer.com/article/10.1007/s10915-023-02120-w
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7616
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spelling oai:localhost:PNK-76162023-04-06T03:10:03Z ReLU Neural Network Galerkin BEM Rubén, Aylwin Fernando, Henríquez Christoph, Schwab ReLU-NNs Galerkin discretization CC BY We introduce Neural Network (NN for short) approximation architectures for the numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN approach for the boundary reduction of the potential problem in two spatial dimensions. We adopt a Galerkin formulation-based method, in polygonal domains with a finite number of straight sides. Trial spaces used in the Galerkin discretization of the BIEs are built by using NNs that, in turn, employ the so-called Rectified Linear Units (ReLU) as the underlying activation function. The ReLU-NNs used to approximate the solutions to the BIEs depend nonlinearly on the parameters characterizing the NNs themselves. 2023-04-06T03:10:02Z 2023-04-06T03:10:02Z 2023 Book https://link.springer.com/article/10.1007/s10915-023-02120-w https://dlib.phenikaa-uni.edu.vn/handle/PNK/7616 en application/pdf Springer
institution Digital Phenikaa
collection Digital Phenikaa
language English
topic ReLU-NNs
Galerkin discretization
spellingShingle ReLU-NNs
Galerkin discretization
Rubén, Aylwin
Fernando, Henríquez
Christoph, Schwab
ReLU Neural Network Galerkin BEM
description CC BY
format Book
author Rubén, Aylwin
Fernando, Henríquez
Christoph, Schwab
author_facet Rubén, Aylwin
Fernando, Henríquez
Christoph, Schwab
author_sort Rubén, Aylwin
title ReLU Neural Network Galerkin BEM
title_short ReLU Neural Network Galerkin BEM
title_full ReLU Neural Network Galerkin BEM
title_fullStr ReLU Neural Network Galerkin BEM
title_full_unstemmed ReLU Neural Network Galerkin BEM
title_sort relu neural network galerkin bem
publisher Springer
publishDate 2023
url https://link.springer.com/article/10.1007/s10915-023-02120-w
https://dlib.phenikaa-uni.edu.vn/handle/PNK/7616
_version_ 1762456092161343488
score 8.881002

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