GLENN

Conda environment for the FE-solver and interpolation:

conda create --name gle-nn 
conda install -c conda-forge fenics-dolfinx mpich pyvista scipy numpy matplotlib pandas pytorch python-gmsh adios4dolfinx
pip install pykan scikit-learn pyyaml tqdm

Python virtual env for training the NNs:

python3.11 -m venv "GLENN"
source GLENN/bin/activate
python -m pip install --upgrade pip
pip3 install torch==2.9 torchvision --index-url https://download.pytorch.org/whl/cu126
pip install tensorboard lightning scipy pyyaml matplotlib

Reproducing the experiments:

Configuration files:

For each of the experiments we provide the necessary configurations. In the following, you find a table mapping the neural networks used in the experiments to the corresponding config file.

Any configuration beyond what is provided in our configuration files is to be treated as unfinished and untested.

Model	GLENN-R1	GLENN-R2	GLENN-F1	GLENN-F2	GLENN-L*	GLENN-U*
File	config_GLENN-R1.yml	config_GLENN-R2.yml	config_GLENN-F1.yml	config_GLENN-F2.yml	config_GLENN-L*.yml	config_GLENN-U*.yml

The star is to be replaced with * = 1,...,5.

Running the experiments:

• The code for training a NN is executed by using

  python main.py --path_to_config <config_file_name> --config_key <top_key_in_config_file> --mode Train

  with the appropriate config file and top level key, e.g.:

  python main.py --path_to_config config_GLENN-R1.yml --config_key GLENN-R1 --mode Train

• Analogously, the interpolation can be done using:

  python main.py --path_to_config <config_file_name> --config_key <top_key_in_config_file> --mode Interpolate

  Here, under the key "loading_config_for_FEM", the kappa for which the neural network is interpolated has to be adapted prior to interpolation. Additionally, under the key "problem_dict", the kappa value has to match this value.

• The solver is run via:

  mpirun -np <number_of_processors> python main.py --path_to_config <config_file_name> --config_key <top_key_in_config_file> --mode Solve

  For the heuristic initial values, set "use_NN_initial_guess" to False and "u_type" to 11,12,13,14, or 15, corresponding to $\varphi_1,...,\varphi_5$. For NN initial values, one has to interpolate a NN first as described in the previous point. Under the key "problem_dict", the value for kappa that the solver uses has to be adapted to the desired parameter.

  For example, to solve with 16 processes using a previously interpolated GLENN-R1 checkpoint, one should use:

  mpirun -np 16 python main.py --path_to_config config_GLENN-R1.yml --config_key GLENN-R1 --mode Solve