Neural network guided adjoint computations in dual weighted residual error estimation

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Roth, J.; Schröder, M.; Wick, T.: Neural network guided adjoint computations in dual weighted residual error estimation. In: SN applied sciences 4 (2022), Nr. 2, 62. DOI:

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Sum total of downloads: 176

In this work, we are concerned with neural network guided goal-oriented a posteriori error estimation and adaptivity using the dual weighted residual method. The primal problem is solved using classical Galerkin finite elements. The adjoint problem is solved in strong form with a feedforward neural network using two or three hidden layers. The main objective of our approach is to explore alternatives for solving the adjoint problem with greater potential of a numerical cost reduction. The proposed algorithm is based on the general goal-oriented error estimation theorem including both linear and nonlinear stationary partial differential equations and goal functionals. Our developments are substantiated with some numerical experiments that include comparisons of neural network computed adjoints and classical finite element solutions of the adjoints. In the programming software, the open-source library deal.II is successfully coupled with LibTorch, the PyTorch C++ application programming interface.
License of this version: CC BY 4.0 Unported
Document Type: Article
Publishing status: publishedVersion
Issue Date: 2022
Appears in Collections:Fakultät für Mathematik und Physik

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pos. country downloads
total perc.
1 image of flag of Germany Germany 86 48.86%
2 image of flag of United States United States 26 14.77%
3 image of flag of China China 9 5.11%
4 image of flag of France France 5 2.84%
5 image of flag of No geo information available No geo information available 4 2.27%
6 image of flag of Iran, Islamic Republic of Iran, Islamic Republic of 4 2.27%
7 image of flag of Indonesia Indonesia 4 2.27%
8 image of flag of South Africa South Africa 3 1.70%
9 image of flag of Thailand Thailand 3 1.70%
10 image of flag of Netherlands Netherlands 3 1.70%
    other countries 29 16.48%

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