Start to Methods

Methods in mUQSA define a scheme of processing required for specific goal related to Uncertainty Quantification or Sensitivity Analysis of computational models. The input to a given method is a set of input parameters, and the result is statistical data, eventually transferred into a form of interactive web page. The methods can be variously configured and adjusted to reach a specific goal.

Main methods supported by mUQSA #

mUQSA currently supports several popular methods for Uncertainty Quantification and Sensitivity Analysis based on the forward uncertainty propagation paradigm, i.e.:

• Monte Carlo with Saltelli sampling (MC)
• Polynomial Chaos Expansion (PCE)
• Stochastic Collocation (SC)

These methods provide valuable descriptive information regarding the uncertainty of model results. They yield key statistics such as the mean, standard deviation, and quantiles, which offer insights into the distribution and spread of the output variables. Additionally, these methods allow for the calculation of Sobol’s indices, which provide valuable understanding of how sensitive the model is to variations in specific parameters. By analyzing these indices, one can gain insight into the relative importance and impact of different input parameters on the model’s output.

The principle behind these methods is to sample the input parameter space and use statistical analysis to estimate the model output distribution. Monte Carlo generates random input parameter sets, while PCE and Stochastic Collocation for the generation of samples use polynomial expansions and deterministic points, respectively.

Since each of the above methods is based on sampling, it requires numerous of evaluations of a model to provide reliable results. The number of required evaluations depends not only on the specific circumstances of a scenario (number of parameters, expected precision, possible resource utilisation, etc.), but also on the method itself and its configuration.

For a closer look at the scientific details of each of the above methods, please see dedicated sections.

Supplementary methods #

mUQSA offers two additional methods for conducting simple analyses of uncertainty and variability in models, namely:

• Basic analysis,
• Parameter sweep analysis.

The Basic analysis method produces a picture of running a model with the same input data multiple times. With this method the parameter space is not sampled, but fixed values are used. This may be useful to check internal variability of the model.

The Parameter sweep analysis involves iteratively running a model or simulation while changing one or more input parameters in accordance with a predetermined range. By exploring the model’s response on systematically changed values of parameters, the method can provide a global overview of the model behaviour. Please note that the fine-grained exploration of multiple parameters will require a large number of evaluations.

What we do not offer #

mUQSA currently focuses on methods supporting non-intrusive scenarios (a model is evaluated as a black-box) and those based on so-called forward-propagation of uncertainty. The methods for intrusive UQ as well as the methods for backward-propagation of uncertainty are currently out-of-scope of the functionality offered by the mUQSA portal. mUQSA also doesn’t support methods for Verification and Validation.

Moreover, since the interface of mUQSA has been designed to be intuitive and can help in both easy definition of multiple advanced configuration parameters required for typical UQ/SA scenarios and analysis of results in a user-friendly way, it has some natural technological limitations. Likewise, despite our best intentions to cover typical requirements of scenarios we want to support, we have not been able to discover all specific circumstances and requirements of the use-cases, and therefore some of the anticipated features may not yet be available.

For these reasons, in all situations where the portfolio of provided methods falls short or if some functionality of the mUQSA portal is not sufficient or broken, we recommend to follow the following algorithms:

1. If you think there is a bug in mUQSA:
   • Contact us.
2. If you think that there is a lack of some method or lack of some configuration option for a certain method:
   • If you need it to be available in mUQSA portal:
     • Contact us
   • If you may use another tool:
     • Check if this option is available in EasyVVUQ
       • If yes:
         • Consider usage of EasyVVUQ from commandline,
         • Contact us if you would like this method or configuration option to be added to mUQSA.
       • if no:
         • Look around for an alternative solution that provides the requested functionality (e.g. Dakota)