uncertainty-propagation: Tools to propagate parameter uncertainty through deterministic black-box functions

The uncertainty-propagation library provides efficient and scalable methods for approximating the output distribution of $Y=f(X)$, i.e. the probability $P(Y \leq y)$, when the input $X$ is a random variable with a known distribution. It is especially useful for complex, black-box functions where analytical solutions are infeasible. Methods like Monte Carlo simulation, directional simulation, and subset simulation as well as first-order reliability method and importance sampling are integrated to provide flexible and scalable uncertainty propagation.

Visual example

Consider the 2-d Rastrigin function:

Animations below show how directional and subset simulation tackle the same problem in different ways, achieving similar approximation accuracy with a fraction of the Monte Carlo sample budget:

Features

• Optimized for Speed: Uses parallelization to maximize performance.
• Minimal Dependencies: Built with as few dependencies as possible.
• Machine Learning Friendly: Designed to integrate seamlessly with machine learning applications using vectorized function calls.
• Extensible Framework: Easily integrate new methods and benchmark different approaches.

Installation

Install the package from PyPI using

pip install uncertainty-propagation

Usage

Documentation is under construction and will soon be available on ReadTheDocs. In the meantime, explore the examples or dive into the source code to see the library in action.

Citing

If this repository has assisted you in your research, please consider citing one of the following works:

• Journal Paper on Uncertainty Optimization:

@Article{Bogoclu2021,
  title       = {Local {L}atin hypercube refinement for multi-objective design uncertainty optimization},
  author      = {Can Bogoclu and Tamara Nestorovi{\'c} and Dirk Roos},
  journal     = {Applied Soft Computing},
  year        = {2021},
  arxiv       = {2108.08890},
  doi         = {10.1016/j.asoc.2021.107807},
  pdf         = {https://www.sciencedirect.com/science/article/abs/pii/S1568494621007286},
}

• PhD Thesis on Uncertainty Quantification and Optimization:

@phdthesis{Bogoclu2022,
  title       = {Local {L}atin hypercube refinement for uncertainty quantification and optimization: {A}ccelerating the surrogate-based solutions using adaptive sampling},
  author      = {Bogoclu, Can},
  school      = {Ruhr-Universit\"{a}t Bochum},
  type         = {PhD thesis},
  year        = {2022},
  doi         = {10.13154/294-9143},
  pdf         = {https://d-nb.info/1268193348/34},
}