# Benchmarks **URL:** https://uqworld.org/c/uq-resources/benchmarks/29.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/3726)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 3, 2024, 11:20am UTC](https://uqworld.org/t/about-the-benchmarks-category/3726 "2024-07-03T11:20:17Z")
Welcome to our repository of functions and datasets used in various UQ benchmark studies. This collection is continuously expanding with new data. We invite you to contribute your own benchmark cases, datasets, competito… --- ## [Benchmark case - Borehole function](https://uqworld.org/t/benchmark-case-borehole-function/3738)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 8, 2024, 10:11am UTC](https://uqworld.org/t/benchmark-case-borehole-function/3738 "2024-07-08T10:11:40Z")
The original post can be found here. The 8-dimensional borehole function models the water flow through a borehole that is drilled from the ground surface through two aquifers. The water flow rate is described by the b… --- ## [Metamodel performance measures](https://uqworld.org/t/metamodel-performance-measures/3771)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [August 13, 2024, 1:40pm UTC](https://uqworld.org/t/metamodel-performance-measures/3771 "2024-08-13T13:40:06Z")
Post-prediction Evaluation Metrics Relative Mean-Squared Error (RelMSE) The relative mean-squared error is calculated as: \\text{RelMSE} = \\frac{\\sum\_{i=1}^{N} (y\_i - \\hat{y}\_i)^2}{\\sum\_{i=1}^{N} (y\_i - \\bar{y})^2}, wh… --- ## [Benchmark case - Two-dimensional heat diffusion model](https://uqworld.org/t/benchmark-case-two-dimensional-heat-diffusion-model/3733)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 4, 2024, 9:56am UTC](https://uqworld.org/t/benchmark-case-two-dimensional-heat-diffusion-model/3733 "2024-07-04T09:56:36Z")
The two-dimensional heat diffusion model The two-dimensional heat diffusion model has been used by Konakli and Sudret (2016) to test the performance of global sensitivity analysis using low-rank tensor approximations and… --- ## [Benchmark case - Morris function](https://uqworld.org/t/benchmark-case-morris-function/3731)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 4, 2024, 8:03am UTC](https://uqworld.org/t/benchmark-case-morris-function/3731 "2024-07-04T08:03:12Z")
Morris function The Morris function has been used by Lamboni et al. (2012), Morris (1991) and Blatman and Sudret (2010) to test the performance of sensivity analyses. Description The performance function is defined as: … --- ## [Benchmark case - Damped Oscillator](https://uqworld.org/t/benchmark-case-damped-oscillator/3730)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 4, 2024, 7:33am UTC](https://uqworld.org/t/benchmark-case-damped-oscillator/3730 "2024-07-04T07:33:59Z")
Damped Oscillator The Damped Oscillator is an example that is commonly used in structural reliability to demonstrate the robustness of the proposed approach for estimating low failure probabilities and their gradients. D… --- ## [Benchmark case - One-dimensional diffusion model](https://uqworld.org/t/benchmark-case-one-dimensional-diffusion-model/3734)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 4, 2024, 12:32pm UTC](https://uqworld.org/t/benchmark-case-one-dimensional-diffusion-model/3734 "2024-07-04T12:32:45Z")
The one-dimensional diffusion model The one-dimensional diffusion model is a standard benchmark in UQ computations used in Shin and Xiu (2016), Fajraoui et al. (2017), and Lüthen et al. (2021). Description This model co… --- ## [Benchmark case - Truss model](https://uqworld.org/t/benchmark-case-truss-model/3729)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 3, 2024, 3:56pm UTC](https://uqworld.org/t/benchmark-case-truss-model/3729 "2024-07-03T15:56:20Z")
Truss model The 23-bar planar truss bridge (Blatman and Sudret, 2011) is a simply supported structure. Bars are categorized into two groups: the first group consists of 11 members, including the upper and lower chords, w… --- ## [Benchmark case - Ishigami function](https://uqworld.org/t/benchmark-case-ishigami-function/3739)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 8, 2024, 10:16am UTC](https://uqworld.org/t/benchmark-case-ishigami-function/3739 "2024-07-08T10:16:55Z")
The original post can be found here. 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; Ma… --- ## [Benchmark case - Wing weight function](https://uqworld.org/t/benchmark-case-wing-weight-function/3728)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 3, 2024, 3:04pm UTC](https://uqworld.org/t/benchmark-case-wing-weight-function/3728 "2024-07-03T15:04:58Z")
Wing weight function The wing weight analytical function provides an estimate of the weight of a light aircraft wing, with input values derived from estimates for a Cessna C172 Skyhawk aircraft. The chosen ranges for eac… --- ## [Benchmark case - 100D function](https://uqworld.org/t/benchmark-case-100d-function/3732)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 4, 2024, 9:00am UTC](https://uqworld.org/t/benchmark-case-100d-function/3732 "2024-07-04T09:00:38Z")
100D function The 100-dimensional function is a high-dimensional function derived from a more generic example detailed below. This function was designed for sensitivity analysis: the first-order sensitivity indices of th… --- ## [Benchmark case - Undamped Oscillator](https://uqworld.org/t/benchmark-case-undamped-oscillator/3727)
**Author:** [@Adela](https://uqworld.org/u/Adela)\ **Replies:** 0\ **Last updated:** [July 3, 2024, 2:09pm UTC](https://uqworld.org/t/benchmark-case-undamped-oscillator/3727 "2024-07-03T14:09:19Z")
Undamped (Gayton) Oscillator The undamped oscillator (Echard et al., 2013) was proposed as a performance function to compare different algorithms for computation of the probability of failure. It is a non-linear, undampe…