Source code for gemseo_umdo.formulations.sequential_sampling

# Copyright 2021 IRT Saint Exupéry,
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# Lesser General Public License for more details.
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
r"""Sequential sampling for multidisciplinary design problems under uncertainty.

is an [UMDOFormulation][gemseo_umdo.formulations.formulation.UMDOFormulation]
estimating the statistics with sequential (quasi) Monte Carlo techniques.

$\mathbb{E}[f(x,U)] \approx \frac{1}{N_k}\sum_{i=1}^{N_k} f\left(x,U^{(k,i)}\right)$
$\mathbb{V}[f(x,U)] \approx
\frac{1}{N_k-1}\sum_{i=1}^{N_k} \left(f\left(x,U^{(k,i)}\right)-
\frac{1}{N_k}\sum_{j=1}^{N_k} f\left(x,U^{(k,j)}\right)\right)^2$
where $U$ is normally distributed
with mean $\mu$ and variance $\sigma^2$
and $U^{(k,1)},\ldots,U^{(k,N_k)}$ are $N_k$ realizations of $U$
obtained at the $k$-th iteration of the optimization loop
with an optimized Latin hypercube sampling technique.
from __future__ import annotations

from typing import Any
from typing import Mapping
from typing import Sequence

from gemseo.algos.design_space import DesignSpace
from gemseo.algos.opt_problem import OptimizationProblem
from gemseo.algos.parameter_space import ParameterSpace
from gemseo.core.discipline import MDODiscipline
from gemseo.core.formulation import MDOFormulation

from gemseo_umdo.formulations.sampling import Sampling

[docs]class SequentialSampling(Sampling): """Sequential sampling-based robust MDO formulation.""" def __init__( self, disciplines: Sequence[MDODiscipline], objective_name: str, design_space: DesignSpace, mdo_formulation: MDOFormulation, uncertain_space: ParameterSpace, objective_statistic_name: str, n_samples: int, initial_n_samples: int = 1, n_samples_increment: int = 1, objective_statistic_parameters: Mapping[str, Any] | None = None, maximize_objective: bool = False, grammar_type: MDODiscipline.GrammarType = MDODiscipline.GrammarType.JSON, algo: str = "OT_OPT_LHS", algo_options: Mapping[str, Any] | None = None, seed: int = 1, **options: Any, ) -> None: """ Args: initial_n_samples: The initial sampling size. n_samples_increment: The increment of the sampling size. """ # noqa: D205 D212 D415 super().__init__( disciplines, objective_name, design_space, mdo_formulation, uncertain_space, objective_statistic_name, initial_n_samples, objective_statistic_parameters=objective_statistic_parameters, maximize_objective=maximize_objective, grammar_type=grammar_type, algo=algo, algo_options=algo_options, seed=seed, **options, ) self.__final_n_samples = n_samples self.__n_samples_increment = n_samples_increment
[docs] def compute_samples(self, problem: OptimizationProblem) -> None: # noqa: D102 super().compute_samples(problem) if self._n_samples < self.__final_n_samples: self._n_samples = min( self.__final_n_samples, self._n_samples + self.__n_samples_increment )