gemseo

# gemseo.uncertainty¶

Uncertainty quantification and management.

The package uncertainty provides several functionalities to quantify and manage uncertainties. Most of them can be used from the high-level functions provided by this module.

The sub-package distributions offers an abstract level for probability distributions, as well as interfaces to the OpenTURNS and SciPy ones. It is also possible to fit a probability distribution from data or select the most likely one from a list of candidates. These distributions can be used to define random variables in a ParameterSpace before propagating these uncertainties through a system of MDODiscipline, by means of a DOEScenario.

The sub-package sensitivity offers an abstract level for sensitivity analysis, as well as concrete features. These sensitivity analyses compute indices by means of various methods: correlation measures, Morris technique and Sobol’ variance decomposition. This sub-package is based in particular on OpenTURNS.

The sub-package statistics offers an abstract level for statistics, as well as parametric and empirical versions. Empirical statistics are estimated from a Dataset while parametric statistics are analytical properties of a Distribution fitted from a Dataset.

gemseo.uncertainty.create_distribution(variable, distribution_name, dimension=1, **options)[source]

Create a distribution.

Parameters:
• variable (str) – The name of the random variable.

• distribution_name (str) – The name of a class implementing a probability distribution, e.g. ‘OTUniformDistribution’ or ‘SPDistribution’.

• dimension (int) –

The dimension of the random variable.

By default it is set to 1.

• **options – The distribution options.

Return type:

Distribution

Examples

>>> from gemseo.uncertainty import create_distribution
>>>
>>> distribution = create_distribution(
...     "x", "OTNormalDistribution", dimension=2, mu=1, sigma=2
... )
>>> print(distribution)
Normal(mu=1, sigma=2)
>>> print(distribution.mean, distribution.standard_deviation)
[1. 1.] [2. 2.]
>>> samples = distribution.compute_samples(10)
>>> print(samples.shape)
(10, 2)

gemseo.uncertainty.create_sensitivity_analysis(analysis, disciplines, parameter_space, **options)[source]

Create the sensitivity analysis.

Parameters:
• analysis (str) – The name of a sensitivity analysis class.

• disciplines (Collection[MDODiscipline]) – The disciplines.

• parameter_space (ParameterSpace) – A parameter space.

• **options – The DOE algorithm options.

Returns:

The toolbox for these sensitivity indices.

Return type:

SensitivityAnalysis

Examples

>>> from gemseo import create_discipline, create_parameter_space
>>> from gemseo.uncertainty import create_sensitivity_analysis
>>>
>>> expressions = {"y1": "x1+2*x2", "y2": "x1-3*x2"}
>>> discipline = create_discipline(
...     "AnalyticDiscipline", expressions=expressions
... )
>>>
>>> parameter_space = create_parameter_space()
...     "x1", "OTUniformDistribution", minimum=-1, maximum=1
... )
...     "x2", "OTNormalDistribution", mu=0.5, sigma=2
... )
>>>
>>> analysis = create_sensitivity_analysis(
...     "CorrelationIndices", [discipline], parameter_space, n_samples=1000
... )
>>> indices = analysis.compute_indices()

gemseo.uncertainty.create_statistics(dataset, variable_names=None, tested_distributions=None, fitting_criterion='BIC', selection_criterion='best', level=0.05, name=None)[source]

Create a statistics toolbox, either parametric or empirical.

If parametric, the toolbox selects a distribution from candidates, based on a fitting criterion and on a selection strategy.

Parameters:
• dataset (Dataset) – A dataset.

• variable_names (Iterable[str] | None) – The variables of interest. If None, consider all the variables from dataset.

• tested_distributions (Sequence[str] | None) – The names of the tested distributions.

• fitting_criterion (str) –

The name of a goodness-of-fit criterion, measuring how the distribution fits the data. Use ParametricStatistics.get_criteria() to get the available criteria.

By default it is set to “BIC”.

• selection_criterion (str) –

The name of a selection criterion to select a distribution from candidates. Either ‘first’ or ‘best’.

By default it is set to “best”.

• level (float) –

A test level, i.e. the risk of committing a Type 1 error, that is an incorrect rejection of a true null hypothesis, for criteria based on a test hypothesis.

By default it is set to 0.05.

• name (str | None) – A name for the statistics toolbox instance. If None, use the concatenation of class and dataset names.

Returns:

A statistics toolbox.

Return type:

Statistics

Examples

>>> from gemseo import (
...     create_discipline,
...     create_parameter_space,
...     create_scenario
... )
>>> from gemseo.uncertainty import create_statistics
>>>
>>> expressions = {"y1": "x1+2*x2", "y2": "x1-3*x2"}
>>> discipline = create_discipline(
...     "AnalyticDiscipline", expressions=expressions
... )
>>>
>>> parameter_space = create_parameter_space()
...     "x1", "OTUniformDistribution", minimum=-1, maximum=1
... )
...     "x2", "OTNormalDistribution", mu=0.5, sigma=2
... )
>>>
>>> scenario = create_scenario(
...     [discipline],
...     "DisciplinaryOpt",
...     "y1",
...     parameter_space,
...     scenario_type="DOE"
... )
>>> scenario.execute({'algo': 'OT_MONTE_CARLO', 'n_samples': 100})
>>>
>>> dataset = scenario.to_dataset(opt_naming=False)
>>>
>>> statistics = create_statistics(dataset)
>>> mean = statistics.compute_mean()

gemseo.uncertainty.get_available_distributions()[source]

Get the available distributions.

Return type:

list[str]

gemseo.uncertainty.get_available_sensitivity_analyses()[source]

Get the available sensitivity analyses.

Return type:

list[str]

Load a sensitivity analysis from the disk.

Parameters:

file_path (str | Path) – The path to the file.

Returns:

The sensitivity analysis.

Return type:

SensitivityAnalysis