# Benchmarks **URL:** https://uqworld.org/c/uq-with-uqlab/benchmarks/19.md [Latest](https://uqworld.org/latest.md) · [Categories](https://uqworld.org/categories.md) · [Tags](https://uqworld.org/tags.md) --- ## [About the Benchmarks category](https://uqworld.org/t/about-the-benchmarks-category/52)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 3\ **Last updated:** [July 9, 2020, 2:24am UTC](https://uqworld.org/t/about-the-benchmarks-category/52 "2020-07-09T02:24:53Z")
Library of test functions and data sets to test your uncertainty quantification (UQ) algorithms. You know additional test functions or data sets? Share them by creating a new topic here! Read this post further for an ind… --- ## [Borehole Function](https://uqworld.org/t/borehole-function/60)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [January 25, 2019, 4:29pm UTC](https://uqworld.org/t/borehole-function/60 "2019-01-25T16:29:57Z")
The 8-dimensional borehole function models water flow through a borehole that is drilled from the ground surface through the two aquifers. The water flow rate is described by the borehole and the aquifer’s properties. … --- ## [High-dimensional Example Function](https://uqworld.org/t/high-dimensional-example-function/67)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [January 29, 2019, 2:21pm UTC](https://uqworld.org/t/high-dimensional-example-function/67 "2019-01-29T14:21:48Z")
The high-dimensional limit state function is used to test algorithms in structural reliability analysis, such as Adaptive Kriging Monte Carlo simulation (AK-MCS) and others (Rackwitz, 2001). A prominent feature of this… --- ## [Infinite Slope Model](https://uqworld.org/t/infinite-slope-model/102)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [February 1, 2019, 1:54pm UTC](https://uqworld.org/t/infinite-slope-model/102 "2019-02-01T13:54:06Z")
The infinite slope model is a 6-dimensional test function for reliability analysis methods. The model is used in geotechnical engineering to quantify the stability of a sloped soil under the influence of water infiltra… --- ## [Exp-Tanh Function](https://uqworld.org/t/exp-tanh-function/56)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [January 24, 2019, 6:07pm UTC](https://uqworld.org/t/exp-tanh-function/56 "2019-01-24T18:07:16Z")
In Owen et al. (2017), the Exp-Tanh function is used to test metamodeling approaches, namely polynomial chaos expansions and Gaussian process modeling. Description The Exp-Tanh function is defined as: f(\\mathbf{x}) … --- ## [Branin Function](https://uqworld.org/t/branin-function/53)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [January 24, 2019, 3:00pm UTC](https://uqworld.org/t/branin-function/53 "2019-01-24T15:00:13Z")
The Branin function is commonly used as a test function for metamodeling in computer experiments, especially in the context of optimization (Forrester et al., 2008; Picheny et al., 2012). Description The analytic expr… --- ## [Rosenbrock's Function](https://uqworld.org/t/rosenbrocks-function/57)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [January 24, 2019, 6:43pm UTC](https://uqworld.org/t/rosenbrocks-function/57 "2019-01-24T18:43:04Z")
The Rosenbrock’s function, also known as the valey or banana function, is commonly used as a test function for optimization algorithms, particularly for gradient-based algorithms since convergence towards its optimum i… --- ## [Gayton Hat Function](https://uqworld.org/t/gayton-hat-function/54)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [January 24, 2019, 3:20pm UTC](https://uqworld.org/t/gayton-hat-function/54 "2019-01-24T15:20:38Z")
The Gayton hat function is a two-dimensional limit state function used in Echard et al. (2013) as a test function for reliability analysis algorithms. Description The performance function is defined as: f(\\mathbf{x}… --- ## [Composite Gaussians](https://uqworld.org/t/composite-gaussians/112)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [February 12, 2019, 4:13pm UTC](https://uqworld.org/t/composite-gaussians/112 "2019-02-12T16:13:00Z")
The composite Gaussians function is a two-dimensional test function used in metamodeling and reliability analysis exercises (Bichon et al., 2011). Description The composite Gaussians function consists of the following… --- ## [Short Column Function](https://uqworld.org/t/short-column-function/103)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [February 1, 2019, 3:49pm UTC](https://uqworld.org/t/short-column-function/103 "2019-02-01T15:49:27Z")
The 3-dimensional short column function models a short column with a rectangular cross-section (width b and depth h) having uncertain material properties (yield stress Y\_C) and being subjected to uncertain loads (bendi… --- ## [Modified Rastrigin Function](https://uqworld.org/t/modified-rastrigin-function/126)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [April 8, 2019, 7:11am UTC](https://uqworld.org/t/modified-rastrigin-function/126 "2019-04-08T07:11:06Z")
The 2-dimensional modified Rastrigin function is a test function for reliability analysis algorithms (Echard et al., 2011). It is a modification of the Rastrigin function (Mühlenbein et al. 1991) to include positive an… --- ## [Four-Branch Function](https://uqworld.org/t/four-branch-function/59)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [January 25, 2019, 2:01pm UTC](https://uqworld.org/t/four-branch-function/59 "2019-01-25T14:01:20Z")
The 2-dimensional four-branch function is a common benchmark problem in reliability analysis (Schueremans and van Gemert, 2005; Echard et al., 2011; Schöbi et al., 2017). The function describes the failure of a series … --- ## [Ishigami Function](https://uqworld.org/t/ishigami-function/55)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 2\ **Last updated:** [April 15, 2020, 3:26pm UTC](https://uqworld.org/t/ishigami-function/55 "2020-04-15T15:26:38Z")
Ishigami Function The Ishigami function is commonly used as a test function to benchmark global sensitivity analysis methods (Ishigami and Homma, 1990; Sobol’ and Levitan, 1999; Marrel et al., 2009). Description The a… --- ## [Liquid Hydrogen Tank Problem](https://uqworld.org/t/liquid-hydrogen-tank-problem/58)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 3\ **Last updated:** [February 28, 2020, 2:06pm UTC](https://uqworld.org/t/liquid-hydrogen-tank-problem/58 "2020-02-28T14:06:48Z")
The 5-dimensional liquid hydrogen tank problem is a reliability analysis benchmark problem (Bichon et al., 2011). The problem consists in quantifying the failure probability of a liquid hydrogen fuel tank on a space la… --- ## [OTL Circuit Function](https://uqworld.org/t/otl-circuit-function/107)
**Author:** [@damarginal](https://uqworld.org/u/damarginal)\ **Replies:** 0\ **Last updated:** [February 7, 2019, 1:39pm UTC](https://uqworld.org/t/otl-circuit-function/107 "2019-02-07T13:39:49Z")
The six-dimensional OTL circuit function computes the mid-point voltage of an output transformerless (OTL) push-pull circuit. It has been used as a test function in metamodeling (Ben-Ari and Steinberg, 2007) and sensitiv…