GLENN: Neural network-enhanced computation of Ginzburg-Landau energy minimizers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918475162714112 |
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| author | Crocoll, Michael Döding, Christian Dörich, Benjamin Maier, Roland |
| author_facet | Crocoll, Michael Döding, Christian Dörich, Benjamin Maier, Roland |
| contents | In this work, we propose a neural network-enhanced finite element strategy to compute the minimizer of the Ginzburg-Landau energy based on an unsupervised deep Ritz-type strategy. We treat the parameter $κ$ as a variable input parameter to obtain possible minimizers for a large range of $κ$-values. This allows for two possible strategies: 1) The neural network may be extensively trained to work as a stand-alone solver. 2) Neural network results are used as starting values for a subsequent classical iterative minimization procedure. The latter strategy particularly circumvents the missing reliability of the neural network-based approach. Numerical examples are presented that show the potential of the proposed strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19096 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | GLENN: Neural network-enhanced computation of Ginzburg-Landau energy minimizers Crocoll, Michael Döding, Christian Dörich, Benjamin Maier, Roland Numerical Analysis In this work, we propose a neural network-enhanced finite element strategy to compute the minimizer of the Ginzburg-Landau energy based on an unsupervised deep Ritz-type strategy. We treat the parameter $κ$ as a variable input parameter to obtain possible minimizers for a large range of $κ$-values. This allows for two possible strategies: 1) The neural network may be extensively trained to work as a stand-alone solver. 2) Neural network results are used as starting values for a subsequent classical iterative minimization procedure. The latter strategy particularly circumvents the missing reliability of the neural network-based approach. Numerical examples are presented that show the potential of the proposed strategy. |
| title | GLENN: Neural network-enhanced computation of Ginzburg-Landau energy minimizers |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.19096 |