GLENN: Neural network-enhanced computation of Ginzburg-Landau energy minimizers
This work addresses computational challenges in physics simulations for researchers, but it is incremental as it builds on existing neural network and finite element methods.
The authors tackled the problem of computing minimizers of the Ginzburg-Landau energy by proposing a neural network-enhanced finite element strategy, which allows for training as a stand-alone solver or as a starting point for classical methods, with numerical examples demonstrating its potential.
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.