pymor.algorithms.adaptivegreedy

Module Contents

class pymor.algorithms.adaptivegreedy.AdaptiveSampleSet(parameter_space)

Bases: pymor.core.base.BasicObject

An adaptive parameter sample set.

Used by adaptive_weak_greedy.

Methods

map_vertex_to_mu
refine
visualize

class Element(level, center, sample_set)

Methods

refine

refine(sample_set)

map_vertex_to_mu(vertex)

refine(ids)

visualize(vertex_data=None, vertex_inds=None, center_data=None, center_inds=None, volume_data=None, vertex_size=80, vmin=None, vmax=None, new_figure=True)

pymor.algorithms.adaptivegreedy.adaptive_weak_greedy(surrogate, parameter_space, target_error=None, max_extensions=None, validation_mus=0, rho=1.1, gamma=0.2, theta=0.0, visualize=False, visualize_vertex_size=80, pool=None)

Weak greedy basis generation algorithm with adaptively refined training set.

This method extends pyMOR’s default weak_greedy greedy basis generation algorithm by adaptive refinement of the parameter training set according to [HDO11] to prevent overfitting of the approximation basis to the training set. This is achieved by estimating the approximation error on an additional validation set of parameters. If the ratio between the estimated errors on the validation set and the validation set is larger than rho, the training set is refined using standard grid refinement techniques.

Parameters:

• surrogate – See weak_greedy.

• parameter_space – The ParameterSpace for which to compute the approximation basis.

• target_error – See weak_greedy.

• max_extensions – See weak_greedy.

• validation_mus –

  One of the following:

  • a list of Parameters to use as validation set,

  • a positive number indicating the number of random parameters to use as validation set,

  • a non-positive number, indicating the negative number of random parameters to use as validation set in addition to the centers of the elements of the adaptive training set.

• rho – Maximum allowed ratio between maximum estimated error on validation set vs. maximum estimated error on training set. If the ratio is larger, the training set is refined.

• gamma – Weight of the age penalty term in the training set refinement indicators.

• theta – Ratio of training set elements to select for refinement. (One element is always refined.)

• visualize – If True, visualize the refinement indicators. (Only available for 2 and 3 dimensional parameter spaces.)

• visualize_vertex_size – Size of the vertices in the visualization.

• pool – See weak_greedy.

Returns:

data – Dict with the following fields:

extensions:

Number of greedy iterations.

max_errs:

Sequence of maximum errors during the greedy run.

max_err_mus:

The parameters corresponding to max_errs.

max_val_errs:

Sequence of maximum errors on the validation set.

max_val_err_mus:

The parameters corresponding to max_val_errs.

refinements:

Number of refinements made in each extension step.

training_set_sizes:

The final size of the training set in each extension step.

time:

Duration of the algorithm.

pymor.algorithms.adaptivegreedy.rb_adaptive_greedy(fom, reductor, parameter_space, use_error_estimator=True, error_norm=None, target_error=None, max_extensions=None, validation_mus=0, rho=1.1, gamma=0.2, theta=0.0, extension_params=None, visualize=False, visualize_vertex_size=80, pool=None)

Reduced basis greedy basis generation with adaptively refined training set.

This method extends pyMOR’s default rb_greedy greedy reduced basis generation algorithm by adaptive refinement of the parameter training set [HDO11] to prevent overfitting of the reduced basis to the training set as implemented in adaptive_weak_greedy.

Parameters:

• fom – See rb_greedy.

• reductor – See rb_greedy.

• parameter_space – The ParameterSpace for which to compute the reduced model.

• use_error_estimator – See rb_greedy.

• error_norm – See rb_greedy.

• target_error – See weak_greedy.

• max_extensions – See weak_greedy.

• validation_mus – See adaptive_weak_greedy.

• rho – See adaptive_weak_greedy.

• gamma – See adaptive_weak_greedy.

• theta – See adaptive_weak_greedy.

• extension_params – See rb_greedy.

• visualize – See adaptive_weak_greedy.

• visualize_vertex_size – See adaptive_weak_greedy.

• pool – See weak_greedy.

Returns:

data – Dict with the following fields:

rom:

The reduced Model obtained for the computed basis.

extensions:

Number of greedy iterations.

max_errs:

Sequence of maximum errors during the greedy run.

max_err_mus:

The parameters corresponding to max_errs.

max_val_errs:

Sequence of maximum errors on the validation set.

max_val_err_mus:

The parameters corresponding to max_val_errs.

refinements:

Number of refinements made in each extension step.

training_set_sizes:

The final size of the training set in each extension step.

time:

Duration of the algorithm.