Physics-Informed Neural Networks for Computational Mechanics (CompSim-PINN)

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---

                         A Multipurpose Python Framework for Computational Mechanics
                          based on Physics-Informed Neural Networks (PINNs)

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Included examples

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• Euler-Bernoulli beams
  • Dynamic beam equation
  • Static beam equation
• Heat equation problems
• Linear elasticity
  • Four-point bending test
  • Forward and inverse Lamé problem
  • Solid beam
  • 3D hollow sphere subjected to internal pressure
  • 4D problem: 3D hollow sphere under time-dependent loading
• Contact problems
  • 2D contact between an elastic block and a rigid surface
  • 2D Hertzian contact problem
  • 3D single contact patch test
  • 3D cylindrical contact problem
• Large deformation (Deep-energy methods)
  • Solid mechanics
    • Bending beam under shear load (2D)
    • Lamé problem
    • 3D torsion of a square prism
  • Contact mechanics (single-step and incremental loading approaches)
    • Single patch test (2D and 3D)
    • 2D Hertzian contact problem
    • 2D Contact ring example (2D)
    • 3D spherical contact problem
    • 3D torus contact instability problem

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Installation of the DeepXDE package and required libraries

This framework relies on the deepxde package for training PINNs.

Note: If you want to be able to debug your PINN training code and step into functions provided by deepxde, you might want to skip the following instructions and instead install it from source in editable mode. Read their website for instructions on how to do that.

deepxde needs one of the following packages for the backend-calculation.

• PyTorch (preferred backend)
• TensorFlow (not supported by all examples, remaining support might be dropped in the future)

You can specify your backend of choice when seting up this framework by running

• for Tensorflow

$ pip install -e ".[tf]"

• for Pytorch

$ pip install -e ".[torch]"

in the top-level repository folder after cloning.

If you additionally want to install packages for development (i.e., for running unittests or buidling the documentation), you can do so by additionally selecting the dev configuration, e.g.,

$ pip install -e ".[tf,dev]"

Setup with conda

This repository also comes with an env.yaml file to directly create a conda environment with all dependencies. The provided conda environment is configured to include the development dependencies and use tensorflow as backend for PINN training. Here we leverage an installation via conda-forge to be able to install specific versions that are tailored to the available hardware. To create an environment, run

$ conda env create -f env.yaml

in the top-level repository folder after cloning.

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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 pyproject.toml 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 env.yaml which includes all necessary packages.

   conda env create -f env.yaml

3. Activate the generated venv (pinns-for-comp-mech)

   conda activate pinns-for-comp-mech

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 pinns-for-comp-mech (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 pinns-for-comp-mech 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 'CompSim-PINN'

Whenever you use or mention 'CompSim-PINN' in some sort of scientific document/publication/presentation, please cite the following publications. They are publicly avaliable at AMSES and ArXiv.

@article{sahin2024,
  title = {Solving Forward and Inverse Problems of Contact Mechanics Using Physics-Informed Neural Networks},
  author = {Sahin, Tarik and Von Danwitz, Max and Popp, Alexander},
  year = {2024},
  journal = {Advanced Modeling and Simulation in Engineering Sciences},
  volume = {11},
  number = {1},
  pages = {11},
  issn = {2213-7467},
  doi = {10.1186/s40323-024-00265-3},
  date = {2024-05-08}
}

@article{Sahin2024b,
  title={Physics-Informed Neural Networks for Solving Contact Problems in Three Dimensions},
  author={Sahin, Tarik and Wolff, Daniel and Popp, Alexander},
  journal={arXiv preprint arXiv:2412.09022},
  year={2024}
}

Paper results are obtained in hastag: c79d3f24023e36341385f10d728e5a93c925fad3