Neural Networks for the approximation of Euler's elastica

Repository for the paper "Neural Networks for the approximation of Euler's elastica". The preprint of the paper can be found at: https://arxiv.org/abs/2312.00644.

The codebase depends on the dependencies collected in the files "requirements.txt" found in each main folder. To install the necessary packages for each network, run the respective scripts

pip install -r requirements.txt

The codes are organized into 3 main folders:

1. ContinuousNetwork, collecting experiments from Section 5.1 of the manuscript,
2. ContinuousNetworkTheta, collecting experiments from Section 5.2 of the manuscript,
3. DiscreteNetwork, collecting experiments from Section 4.1 of the manuscript.

We add to each of these subdirectories a short readme file to facilitate running the code.

The folder DataSets contains the beam code used to generate the data sets, and the two data sets (both-ends and right-end) mentioned in the paper.

Citation key: @article{celledoni2023neural, title={Neural networks for the approximation of Euler's elastica}, author={Elena Celledoni and Ergys Çokaj and Andrea Leone and Sigrid Leyendecker and Davide Murari and Brynjulf Owren and Rodrigo T. Sato Martín de Almagro and Martina Stavole}, journal={arXiv preprint arXiv:2312.00644}, year={2023} }