gemseo_umdo / formulations

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sampling module

Sampling for multidisciplinary design problems under uncertainty.

Sampling is an UMDOFormulation estimating the statistics with (quasi) Monte Carlo techniques.

E.g. \(\mathbb{E}[f(x,U)] \approx \frac{1}{N}\sum_{i=1}^N f\left(x,U^{(i)}\right)\) or \(\mathbb{V}[f(x,U)] \approx \frac{1}{N}\sum_{i=1}^N \left(f\left(x,U^{(i)}\right)- \frac{1}{N}\sum_{j=1}^N f\left(x,U^{(j)}\right)\right)^2\) where \(U\) is normally distributed with mean \(\mu\) and unit variance \(\sigma\) and \(U^{(1)},\ldots,U^{(1)}\) are \(N\) realizations of \(U\) obtained with an optimized Latin hypercube sampling technique.

class gemseo_umdo.formulations.sampling.Sampling(disciplines, objective_name, design_space, mdo_formulation, uncertain_space, objective_statistic_name, n_samples, objective_statistic_parameters=None, maximize_objective=False, grammar_type=GrammarType.JSON, algo='OT_OPT_LHS', algo_options=None, seed=1, **options)[source]

Bases: UMDOFormulation

Sampling-based robust MDO formulation.

Parameters:

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

  • objective_name (str) – The name(s) of the discipline output(s) used as objective. If multiple names are passed, the objective will be a vector.

  • design_space (DesignSpace) – The design space.

  • mdo_formulation (MDOFormulation) – The class name of the MDO formulation, e.g. “MDF”.

  • uncertain_space (ParameterSpace) – The uncertain variables with their probability distributions.

  • objective_statistic_name (str) – The name of the statistic to be applied to the objective.

  • n_samples (int) – The number of samples, i.e. the size of the DOE.

  • objective_statistic_parameters (Mapping[str, Any] | None) – The values of the parameters of the statistic to be applied to the objective, if any.

  • maximize_objective (bool) –

    Whether to maximize the objective.

    By default it is set to False.

  • grammar_type (MDODiscipline.GrammarType) –

    The type of the input and output grammars.

    By default it is set to “JSONGrammar”.

  • algo (str) –

    The name of the DOE algorithm.

    By default it is set to “OT_OPT_LHS”.

  • algo_options (Mapping[str, Any] | None) – The options of the DOE algorithm.

  • seed (int) –

    The description is missing.

    By default it is set to 1.

  • **options (Any) – The options of the formulation.

compute_samples(problem)[source]

Evaluate the functions of a problem with a DOE algorithm.

Parameters:

problem (OptimizationProblem) – The problem.

Return type:

None

opt_problem: OptimizationProblem

The optimization problem generated by the formulation from the disciplines.