1. pce

This repository includes an implementation of the Polynomial Chaos Expansion method.

1.1 Brief description

More comprehensive tools on the same subject are available (e.g. Chaospy), this repository is born during a self-learning activity of the authors.

At the moment, one can use this module to study the uncertainty propagation of a model with uncertain inputs. The following aspects are implemented:

• each uncertain variable can be associated to a uniform or normal distribution
• evaluation of the coefficient with spectral projection method
• global sensitivity analysis with Sobol' indices

1.2 How can I use it? How can I cite this module?

If you use this module you can consider to cite the following papers:

[1] Luca Giaccone, "Uncertainty quantification in the assessment of human exposure to pulsed or multi-frequency fields", Physics in Medicine & Biology, 10.1088/1361-6560/acc924

[2] Giaccone, L.; Lazzeroni, P.; Repetto, M. Uncertainty Quantification in Energy Management Procedures. Electronics 2020, 9, 1471. https://doi.org/10.3390/electronics9091471

In [1] the pce is used to estimate the uncertainty associated to methods for the assessment of pulsed magnetic or electric fields. You can also find all codes associated to the paper here https://github.com/giaccone/wpm_uncertainty. In [2] the pce module has been used successfully to estimate uncertainties. You can also find all codes associated to the paper here https://github.com/giaccone/cogen_eval.

1.3 Requirements

The project is developed using Python 3. The installer requires a Python version >= 3.6.

Other requirements (I tend to use always the latest version of the following libraries):

• numpy
• scipy
• matplotlib
• joblib

2. Installation

This project is deployed through the Python Package Index, therefore, it can be easily obtained by running the following command:

pip install pce