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pygpc

A Sensitivity and uncertainty analysis toolbox for Python based on the generalized polynomial chaos method

Basic features:

• Highly efficient uncertainty analysis of N-dimensional systems
• Sensitivity analysis using Sobol indices and Global derivative based sensitivity indices
• Easy coupling to user defined models written in Python, Matlab, etc...
• The parallelization concept allows to run model evaluations in parallel
• Highly efficient adaptive algorithms allow for analysis of complex systems
• Includes highly efficient CPU and GPU (CUDA) implementations to significantly accelerate algorithmic and post-processing routines for high-dimensional and complex problems
• Includes state-of-the-art techniques such as:
  • Projection: determination of optimal reduced basis
  • L1-minimization: reduction of necessary model evaluations by making use of concepts from compressed sensing
  • Gradient enhanced gPC: use of gradient information of the model function to increase accuracy
  • Multi-element gPC: analyzing systems with discontinuities and sharp transitions
  • Optimized Latin Hypercube Sampling for fast convergence

Areas of application:

pygpc can be used to analyze a variety of different of problems. It is used for example in the frameworks of:

• Nondestructive testing:

  • Weise, K., Carlstedt, M., Ziolkowski, M., & Brauer, H. (2015). Uncertainty analysis in Lorentz force eddy current testing. IEEE Transactions on Magnetics, 52(3), 1-4.

• Noninvasive brain stimulation:

  • Saturnino, G. B., Thielscher, A., Madsen, K. H., Knösche, T. R., & Weise, K. (2019). A principled approach to conductivity uncertainty analysis in electric field calculations. NeuroImage, 188, 821-834.

• Transcranial magnetic stimulation:

  • Weise, K., Di Rienzo, L., Brauer, H., Haueisen, J., & Toepfer, H. (2015). Uncertainty analysis in transcranial magnetic stimulation using nonintrusive polynomial chaos expansion. IEEE Transactions on Magnetics, 51(7), 1-8.
  • Weise, K., Numssen, O., Thielscher, A., Hartwigsen, G., & Knösche, T. R. (2020). A novel approach to localize cortical TMS effects. NeuroImage, 209, 116486.

• Transcranial direct current stimulation:

  • Kalloch, B., Weise, K., Bazin, P.-L., Lampea, L., Villringera, A., Hlawitschk, M., & Sehm, B. (2019). The influence of white matter lesions on the electrical fieldduring transcranial electric stimulation - Preliminary results of a computational sensitivity analysis, SfN Annual Meeting 2019, Chicago, Illinois, USA, October 19th-23rd 2019

  • Kalloch, B., Weise, K., Lampe, L., Bazin, P. L., Villringer, A., Hlawitschka, M., & Sehm, B. (2022). The influence of white matter lesions on the electric field in transcranial electric stimulation. NeuroImage: Clinical, 103071.

• Cancer treatment

  • Atsou, K., Khou S., Anjuère F., Braud, V., & Thierry Goudon (2022), Analysis of the equilibrium phase in immune-controlled tumors predicts best strategies for cancer treatment, preprint

If you use pygpc in your studies, please contact Konstantin Weise to extend the list above.

Installation

Installation using pip: Pygpc can be installed via the pip command with Python >= 3.6. Simply run the following command in your terminal:

pip install pygpc

If you want to use the plot functionalities of pygpc, please also install matplotlib and seaborn:

pip install matplotlib seaborn

Installation using the GitHub repository: Alternatively, it is possible to clone this repository and run the setup manually. This requires a compiler that supports OpenMP which is used by the C-extensions and NumPy for some headers. You can install NumPy by running the following command:

pip install numpy

Alternatively you can install the build dependencies with the following command:

pip install -r requirements.txt

Afterwards, pygpc can be installed by running the following line from the directory in which the repository was cloned:

python setup.py install

Installation of the CUDA backend: Pygpc also provides a CUDA-backend to speed up some computations. To use the backend you need to build it manually. This requires the CUDA-toolkit and CMake. CMake can be installd via the pip command. Simply run the following command in your terminal:

pip install cmake 

For the installation of the CUDA-toolkit, please refer to this website. If CMake and the CUDA-toolkit are installed on your machine you can build the extension with:

python build_pygpc_extensions_cuda.py 

Troubleshooting for OSX: On a Mac you need GCC to install pygpc. If you are using the brew package manager you can simply run:

brew install gcc libomp 

Then install pygpc with:

CC=gcc-9 CXX=g++-9 python setup.py install 

Troubleshooting for Windows: On windows you might need a compiler to install pygpc. To install the Visual C++ Build Tools, please refer to this website.

Documentation

For a full API of pygpc, see https://pygpc.readthedocs.io/en/latest/. For examplary simulations and model configurations, please have a look at the jupyter notebooks provided in the /tutorial folder and the templates in the /example folder.

Reference

If you use this framework, please cite:

• Weise, K., Poßner, L., Müller, E., Gast, R., & Knösche, T. R. (2020). Pygpc: A sensitivity and uncertainty analysis toolbox for Python. SoftwareX, 11, 100450.

Contact

If you have questions, problems or suggestions regarding pygpc, please contact Konstantin Weise.