UQTestFuns

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UQTestFuns is an open-source Python3 library of test functions commonly used within the applied uncertainty quantification (UQ) community. Specifically, the package provides:

• an implementation with minimal dependencies (i.e., NumPy and SciPy) and a common interface of many test functions available in the UQ literature
• a single entry point collecting test functions and their probabilistic input specifications in a single Python package
• an opportunity for an open-source contribution, supporting the implementation of new test functions or posting reference results.

In short, UQTestFuns is an homage to the Virtual Library of Simulation Experiments (VLSE).

Usage

UQTestFuns includes several commonly used test functions in the UQ community. To list the available functions:

```python-repl

import uqtestfuns as uqtf uqtf.list_functions() +-------+-------------------------------+-----------+------------+----------+---------------+--------------------------------+ | No. | Constructor | # Input | # Output | Param. | Application | Description | +=======+===============================+===========+============+==========+===============+================================+ | 1 | Ackley() | M | 1 | True | optimization, | Optimization test function | | | | | | | metamodeling | from Ackley (1987) | +-------+-------------------------------+-----------+------------+----------+---------------+--------------------------------+ | 2 | Alemazkoor20D() | 20 | 1 | False | metamodeling | High-dimensional low-degree | | | | | | | | polynomial from Alemazkoor & | | | | | | | | Meidani (2018) | +-------+-------------------------------+-----------+------------+----------+---------------+--------------------------------+ | 3 | Alemazkoor2D() | 2 | 1 | False | metamodeling | Low-dimensional high-degree | | | | | | | | polynomial from Alemazkoor & | | | | | | | | Meidani (2018) | +-------+-------------------------------+-----------+------------+----------+---------------+--------------------------------+ | 4 | Borehole() | 8 | 1 | False | metamodeling, | Borehole function from Harper | | | | | | | sensitivity | and Gupta (1983) | +-------+-------------------------------+-----------+------------+----------+---------------+--------------------------------+ ... ```

Consider the Borehole function, a test function commonly used for metamodeling and sensitivity analysis purposes; to create an instance of this test function:

```python-repl

mytestfun = uqtf.Borehole() print(mytestfun) Function ID : Borehole Input Dimension : 8 (fixed) Output Dimension : 1 Parameterized : False Description : Borehole function from Harper and Gupta (1983) Applications : metamodeling, sensitivity ```

The probabilistic input specification of this test function is built-in:

```python-repl

print(mytestfun.probinput) Function ID : Borehole Input ID : Harper1983 Input Dimension : 8 Description : Probabilistic input model of the Borehole model from Harper and Gupta (1983) Marginals :

No. Name Distribution Parameters Description

1 rw normal [0.1 0.0161812] radius of the borehole [m] 2 r lognormal [7.71 1.0056] radius of influence [m] 3 Tu uniform [ 63070. 115600.] transmissivity of upper aquifer [m^2/year] 4 Hu uniform [ 990. 1100.] potentiometric head of upper aquifer [m] 5 Tl uniform [ 63.1 116. ] transmissivity of lower aquifer [m^2/year] 6 Hl uniform [700. 820.] potentiometric head of lower aquifer [m] 7 L uniform [1120. 1680.] length of the borehole [m] 8 Kw uniform [ 9985. 12045.] hydraulic conductivity of the borehole [m/year]

Copulas : Independence ```

A sample of input values can be generated from the input model:

```python-repl

xx = mytestfun.probinput.get_sample(10) array([[8.40623544e-02, 2.43926544e+03, 8.12290909e+04, 1.06612711e+03, 7.24216436e+01, 7.78916695e+02, 1.13125867e+03, 1.02170796e+04], [1.27235295e-01, 3.28026293e+03, 6.36463631e+04, 1.05132831e+03, 6.81653728e+01, 8.17868370e+02, 1.16603931e+03, 1.09370944e+04], [8.72711602e-02, 7.22496512e+02, 9.18506063e+04, 1.06436843e+03, 6.44306474e+01, 7.74700231e+02, 1.46266808e+03, 1.12531788e+04], [1.22301709e-01, 2.29922122e+02, 8.00390345e+04, 1.05290108e+03, 1.10852262e+02, 7.94709283e+02, 1.28026313e+03, 1.01879077e+04], ... ```

...and used to evaluate the test function:

```python-repl

yy = my_testfun(xx) array([ 57.32635774, 110.12229548, 53.10585812, 96.15822154, 58.51714875, 89.40068404, 52.61710076, 61.47419171, 64.18005235, 79.00454634]) ```

Installation

You can obtain UQTestFuns directly from PyPI using pip:

bash $ pip install uqtestfuns

Alternatively, you can also install the latest version from the source:

bash pip install git+https://github.com/damar-wicaksono/uqtestfuns.git

NOTE: UQTestFuns is currently work in progress, therefore interfaces are subject to change.

It's a good idea to install the package in an isolated virtual environment.

Getting help

For a getting-started guide on UQTestFuns, please refer to the Documentation. The documentation also includes details on each of the available test functions.

For any other questions related to the package, post your questions on the GitHub Issue page.

Package development and contribution

UQTestFuns is under ongoing development; any contribution to the code (for example, a new test function) and the documentation (including new reference results) are welcomed!

Please consider the Contribution Guidelines first, before making a pull request.

Citing UQTestFuns

If you use this package in your research or projects, please consider citing both the associated paper and the Zenodo archive (for the specific version used).

Citing the paper (JOSS)

The citation of the paper associated with this package is:

bibtex @article{Wicaksono2023, author = {Wicaksono, Damar and Hecht, Michael}, title = {{UQTestFuns}: A {Python3} library of uncertainty quantification ({UQ}) test functions}, journal = {Journal of Open Source Software}, year = {2023}, volume = {8}, number = {90}, doi = {10.21105/joss.05671}, }

Citing a specific version (Zenodo)

To ensure reproducibility, cite the exact version of the package you used. Each release is archived on Zenodo with a unique DOI; find and use the DOI for the version you used at Zenodo.

The citation for the current public version is:

bibtex @software{UQTestFuns_0_6_0, author = {Wicaksono, Damar and Hecht, Michael}, title = {{UQTestFuns: A Python3 Library of Uncertainty Quantification (UQ) Test Functions}}, month = jan, year = 2025, publisher = {Zenodo}, version = {v0.6.0}, doi = {10.5281/zenodo.14710452}, url = {https://doi.org/10.5281/zenodo.14710452} }

Credits and contributors

This work was partly funded by the Center for Advanced Systems Understanding (CASUS) which is financed by Germany's Federal Ministry of Education and Research (BMBF) and by the Saxony Ministry for Science, Culture and Tourism (SMWK) with tax funds on the basis of the budget approved by the Saxony State Parliament.

UQTestFuns is currently maintained by:

• Damar Wicaksono (HZDR/CASUS)

under the Mathematical Foundations of Complex System Science Group led by Michael Hecht (HZDR/CASUS) at CASUS.

License

UQTestFuns is released under the MIT License.