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arXiv · 2603.19096

GLENN: Neural network-enhanced computation of Ginzburg-Landau energy minimizers

Michael Crocoll·Christian Döding·Benjamin Dörich·Roland Maier
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Abstract

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 $\kappa$ as a variable input parameter to obtain possible minimizers for a large range of $\kappa$-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.

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Michael Crocoll, Christian Döding, Benjamin Dörich, Roland Maier. 2026-03-19. GLENN: Neural network-enhanced computation of Ginzburg-Landau energy minimizers. https://arxiv.org/abs/2603.19096

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