Physics-Informed Neural Networks for Computational Mechanics (pinns_for_comp_mech)

Implementation of Physics-Informed Neural Networks for computational mechanics based on the deepXDE package.

• Euler-Bernoulli beams
• Heat equation problems
• Linear elasticity
  • Four-point bending test
  • Forward and inverse Lame` problems
  • Solid beam
• Contact problems
  • Contact between elastic body and rigid flat surface
  • Hertzian contact problem

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Installation of the DeepXDE package and required libraries

  $ pip install -r requirements.txt

Setup the framework using python develop, which will install utils.

   $ python setup.py develop

For more info: deepxde website

Note: DeepXDE needs one of the following packages for the backend-calculation. Read the website for more info.

• Tensorflow
• Pytorch

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Testing

This repo has integration_tests (testing for examples/frameworks) and unittests (testing for specific functions). Testing is done by pytest and tests are configured in the setup.cfg file.

To run tests, type on the terminal:

$ pytest

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Cluster setup

For cluster, we should use conda since we had issues in terms of package installation particularly the package gmsh. Enable pinn repo to run on cluster:

1. Install miniconda https://docs.conda.io/en/latest/miniconda.html :

   wget https://repo.anaconda.com/miniconda/Miniconda3-latest-Linux-x86_64.sh
   ./Miniconda3-latest-Linux-x86_64.sh

2. Create the virtual environment using environment.yml which includes all necessary packages.

   conda env create -f environment.yml

3. Activate the generated venv (pinn-env)

   conda activate pinn-env

4. To test cluster, submit a job on a compute node. This is achieved through test_cluster.sh (full path: pinnswithdxde/tests/integration_tests/cluster/test_cluster.sh).

   $ sbatch $HOME/pinnswithdxde/tests/integration_tests/cluster/test_cluster.sh

   Number of threads is set in test_cluster.sh file. TensorFlow needs to be intra_op_parallelism_threads and inter_op_parallelism_threads parameters set. Thus, we give tf_cluster_settings.py to the slurm job via sbatch. This enables TensorFlow to set OMP parameters that defined in test_cluster.sh.

NOTE: Do not forget to adopt the inside of the test_cluster.sh to specify the slurm options e.g., --mail-user. But the default one should work without error.

NOTE: Always be sure that you activated venv pinn-env (step 3) before sbatch any slurm script. This includes other scripts you will run as well. The reason behind is that activating venv in test_cluster.sh needs the full path for the conda env pinn-env and it gives some init error if the full path is used.

NOTE: For conda commands: A conda cheatsheet can be very useful.

NOTE: Some usefull information regarding CPU on cluster.

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Citing 'pinns_for_comp_mech'

Whenever you use or mention 'pinns_for_comp_mech' in some sort of scientific document/publication/presentation, please cite the following publication. It is publicly avaliable at arXiv.

@article{sahin2023pinnforcontact,
   title={Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks},
   author={Sahin, Tarik and von Danwitz, Max and Popp, Alexander},
   journal={arXiv preprint arXiv:2308.12716},
   year={2023}
}

Paper results are obtained in hastag: c79d3f24023e36341385f10d728e5a93c925fad3