gemseo_umdo / statistics / multilevel / mlmc_mlcv

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level module

A level $ell$ for the MLMC-MLCV algorithm.

class gemseo_umdo.statistics.multilevel.mlmc_mlcv.level.Level(model, surrogate_model, difference_surrogate_model=(), cost=None, n_cost_estimation_samples=1, n_initial_samples=10, sampling_ratio=2.0)[source]

Bases: object

A level $ell$ for the MLMC-MLCV algorithm.

Parameters:

  • model (MDOFunction) –

  • surrogate_model (tuple[MDOFunction, float]) –

  • difference_surrogate_model (tuple[MDOFunction, float]) –

    By default it is set to ().

  • cost (float | None) –

  • n_cost_estimation_samples (int) –

    By default it is set to 1.

  • n_initial_samples (int) –

    By default it is set to 10.

  • sampling_ratio (float) –

    By default it is set to 2.0.

cost: float | None = None

The cost $mathcal{C}_ell$ to evaluate $f_ell$, if known.

difference_surrogate_model: tuple[MDOFunction, float] = ()

The surrogate model $h_ell$ approximating $f_ell-f_{ell-1}$.

More precisely, $h_ell$ and its statistic for the [MLMCMLCV][gemseo_umdo.statistics.multilevel.mlmc_mlcv.mlmc_mlcv.MLMCMLCV] algorithm.

Empty at level $ell=0$.

The surrogate model can be set from any callable taking a NumPy array of float numbers as input and outputting either a float number or a NumPy array of float numbers.

model: MDOFunction

The model $f_ell$ to sample.

This model can be set from any callable taking a NumPy array of float numbers as input and outputting either a float number or a NumPy array of float numbers.

n_cost_estimation_samples: int = 1

The number of $f_ell$ calls to estimate $mathcal{C}_ell$.

It will be used only if cost is None.

n_initial_samples: int = 10

The number of samples $n_ell$ at the first iteration of the algorithm.

sampling_ratio: float = 2.0

The factor $r_ell$ by which $n_ell$ is increased.

surrogate_model: tuple[MDOFunction, float]

The surrogate model $g_ell$ approximating $f_ell$.

More precisely, $g_ell$ and its statistic for the [MLMCMLCV][gemseo_umdo.statistics.multilevel.mlmc_mlcv.mlmc_mlcv.MLMCMLCV] algorithm.

The surrogate model can be set from any callable taking a NumPy array of float numbers as input and outputting either a float number or a NumPy array of float numbers.