Physics-Informed Neural Networks for Computational Mechanics (compsim_pinns)

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---

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

CompSim_PINNs is a Python framework originated and maintained by the Institute for Mathematics and Computer-Based Simulation (IMCS) at the University of the Bundeswehr Munich.

This framework implements the functionalities of PINNs (Physics-Informed Neural Networks) using the DeepXDE package for solid and contact mechanics.

Note: This framework and and its documentation are under active development.

Examples provided by the framework

• 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

---

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 by this framework)
• TensorFlow (not supported by all examples, remaining support within this framework might be dropped in the future)

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.

Setup with pip

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

• for Pytorch

$ pip install -e ".[torch]"

• for Tensorflow

$ pip install -e ".[tf]"

in the top-level repository folder after cloning.

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

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

---

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 in the terminal:

$ pytest

---

Pre-commit hooks

This repo uses pre-commit to enforce formatting, linting, type checks, and commit message conventions.

Install the git hooks:

$ pre-commit install
$ pre-commit install --hook-type commit-msg

---

Docker image

This framework provides its functionality also in a Docker. To use it that way follow these instructions:
First, build the docker container using Dockerfile and type the following command on the terminal

docker build -t imcs-pinn -f docker/Dockerfile .

Then, run the docker container by typing the following command on the terminal

docker run imcs-pinn

NOTE: The command above will automatically run the default commands defined in Dockerfile.

When you want to open an interactive shell inside the container or interact with the process manually, for instance for debugging, then run

docker run -it imcs-pinn bash

Run, a specific example

docker run -it imcs-pinn conda run -n compsim_pinns python examples/elasticity_3d/linear_elasticity/block_under_shear.py

Citing 'compsim_pinns'

Whenever you use or mention 'compsim_pinns' in some sort of scientific document/publication/presentation, please cite the following publications. They are publicly available at AMSES and Springer Nature.

@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}
}

Results from this paper are obtained in hash c79d3f24023e36341385f10d728e5a93c925fad3.

@incollection{Sahin2025,
  title = {Physics-Informed Neural Networks for Solving Contact Problems in Three Dimensions},
  booktitle = {Advances and Challenges in Computational Mechanics},
  author = {Sahin, Tarik and Wolff, Daniel and Popp, Alexander},
  editor = {Graf, Wolfgang and Fleischhauer, Robert and Storm, Johannes and Wollny, Ines},
  date = {2025},
  pages = {419--431},
  publisher = {Springer Nature Switzerland},
  location = {Cham},
  doi = {10.1007/978-3-031-93213-7_33},
  isbn = {978-3-031-93212-0 978-3-031-93213-7}
}