Detailed Description

class generating the reduced basis space for the LinEvol problem with a Greedy algorithm.

Parameters given by the constructor argument bg_descr can control the

trainings sample (train_sample_mode, train_num_intervals, train_seed)
trainings sample refinement (refinement_mode, max_refinement_level, refinement_theta, val_size, val_seed, stop_max_val_train_ratio)
the error indicator (indicator_mode)
greedy variant selection by Mmax_small
- PODEI-greedy (Mmax_small > 0): small_train_num_intervals, epsilon_M_by_N_r, maximum_temporary_error_growth_factor, ei_minimum_residual, extension_M_by_N_r, ei_epsilon_small
- subsequent generation of EI by EI-greedy and RB by POD-greedy. (Mmax_small == 0)
general EI extension controls (noof_ei_extensions) and
general greedy controls (stop_Nmax, stop_Mmax, stop_timeout, stop_epsilon, stop_max_val_train_ratio)

Definition at line 18 of file DetailedData.m.

Inheritance diagram for NonlinEvol.DetailedData:

[legend]

Collaboration diagram for NonlinEvol.DetailedData:

[legend]

Public Member Functions
	DetailedData (LinEvol.ReducedModel rmodel,ModelData model_data)
	constructor constructing the reduced basis spaces and storing it in a DataTree. More...

function rb_size =	get_rb_size (IReducedModel rmodel)
	returns the dimension of the stored reduced basis space. More...

Public Member Functions inherited from Greedy.User.IDetailedData
	IDetailedData (BasisGenDescr bg_descr,ModelData model_data)
	constructor forwarding the arguments to IDetailedData constructor More...

function Greedy.DataTree.Detailed.ILeafNode detailed_data_leaf =	get_leaf (Greedy.User.IReducedModel rmodel)
	returns the data tree leaf node for a specific combination of parameters and time indices given by a reduced model. More...

Public Member Functions inherited from IDetailedData
	IDetailedData (BasisGenDescr bg_descr, model_data)
	constructor generating the reduced basis spaces More...

function ret =	subsref (S)
	forwarding of fieldnames access to the underlying model_data struct More...

Public Attributes
Greedy.Interface	bg_algorithm
	a basis generation algorithm used to generated the reduced basis space. More...

	train_sample_mode = "uniform"
	flag indicating whether the parameter sampling for the training set \(M_{\text{train}}\) type. More...

	train_num_intervals = 3
	number of intervals in the ParameterSampling.Uniform respectively number of vectors in the ParameterSampling.Random for the training set \(M_{\text{train}}\) of the parameter space \({\cal M}\). More...

	train_seed = 4321
	If `train_sample_mode == random`, a ParameterSampling.Random is generated for the training set \(M_{\text{val}}\) with size train_num_intervals and seed `train_seed`. More...

	refinement_mode = "adaptive"
	sets the Greedy.TrainingSetAdaptation.refinement_mode option More...

	max_refinement_level = 5
	sets the Greedy.TrainingSetAdaptation.max_refinement_level option More...

	refinement_theta = 0.2
	sets the Greedy.TrainingSetAdaptation.refinement_theta option More...

	val_size = 10
	If this value is non-zero, a ParameterSampling.Random is generated for the validation set \(M_{\text{val}}\) with size val_size and seed val_seed. More...

	val_seed = 1234
	If the value of `val_size` is non-zero, a ParameterSampling.Random is generated for the validation set \(M_{\text{val}}\) with size val_size and seed `val_seed`. More...

	small_train_num_intervals = 2
	number of intervals in the ParameterSampling.Uniform for the small training set \(M_{\text{small}}\) for the generation of an initial collateral reduced basis space. More...

	Mmax_small = 10
	sets the Greedy.Plugin.PODEI.Mmax_small member More...

	epsilon_M_by_N_r = 1e-4
	ratio between the stop epsilon criterion for collateral reduced basis spaces and reduced basis spaces. More...

	maximum_temporary_error_growth_factor = 0
	maximum factor between the current maximum indicator and the smallest maximum error indicator during previous extensions More...

	ei_minimum_residual = 1e-8
	sets the Greedy.Plugin.EI.minimum_residual More...

	extension_M_by_N_r = 4
	sets the Greedy.Plugin.PODEI.M_by_N_ratio More...

	ei_epsilon_small = 1e-2
	maximum error between operator interpolations at which the initial value greedy is stopped. More...

	stop_Mmax = 200
	sets the Greedy.Plugin.EI.stop_Mmax option More...

	stop_Nmax = 50
	sets the Greedy.Plugin.PODEI.stop_Nmax option More...

	indicator_mode = "estimator"
	string specifying which indicators shall be used by the error_indicators() method. More...

	stop_epsilon = 1e-5
	sets the Greedy.Algorithm.stop_epsilon option More...

	stop_max_val_train_ratio = 1.2
	sets the Greedy.Algorithm.stop_max_val_train_ratio option More...

	stop_timeout = 126060
	sets the Greedy.Algorithm.stop_timeout option More...

	noof_ei_extensions = 1
	sets the number of ei extensions More...

Public Attributes inherited from Greedy.User.IDetailedData
::Greedy.DataTree.Detailed.INode	datatree
	the actual generated data tree

Public Attributes inherited from IDetailedData
BasisGenDescr	bg_descr
	struct describing how the basis shall be generated. More...

::ModelData	model_data
	struct holding \(H\)-dimensional model data, which is needed for an IDetailedModel.detailed_simulation(), e.g. a grid object.

Constructor & Destructor Documentation

NonlinEvol.DetailedData.DetailedData	(	LinEvol.ReducedModel	rmodel,
		ModelData	model_data
	)

constructor constructing the reduced basis spaces and storing it in a DataTree.

Parameters

rmodel	object specifying how the reduced simulations can be computed.
model_data	Matlab structure storing (possibly) high dimensional data needed by IDetailedModel.detailed_simulation().

Required fields of rmodel:

bg_descr — bg descr
detailed_model — detailed model

Definition at line 338 of file DetailedData.m.

Member Function Documentation

function rb_size = NonlinEvol.DetailedData.get_rb_size ( IReducedModel rmodel )

virtual

returns the dimension of the stored reduced basis space.

Parameters

rmodel model specifying which basis space dimension shall be returned in case different spaces have been generated different parameters, time intervals or variables. In most implementations this parameter is unused.

Return values

rb_size rb size

Implements IDetailedData.

Definition at line 493 of file DetailedData.m.

Here is the call graph for this function:

Member Data Documentation

NonlinEvol.DetailedData.bg_algorithm

a basis generation algorithm used to generated the reduced basis space.

generates a default basis generation object for linear evolution problems as given by a DetailedModel.

Note: This property has the MATLAB attribute Dependent set to true.; This property has non-standard access specifiers: SetAccess = Private, GetAccess = Public; Matlab documentation of property attributes.

This function generates a Greedy.Interface implementation, with either a subsequent generation of empirical interpolation bases spaces for all operators and a reduced basis space afterwards, or a combined generation of all reduced spaces with the Greedy.Plugin.PODEI variant of the Greedy.Algorithm.

Note: [readonly]

Definition at line 49 of file DetailedData.m.

NonlinEvol.DetailedData.ei_epsilon_small = 1e-2

maximum error between operator interpolations at which the initial value greedy is stopped.

See Mmax_small for details.

Default: 1e-2

Definition at line 259 of file DetailedData.m.

NonlinEvol.DetailedData.ei_minimum_residual = 1e-8

sets the Greedy.Plugin.EI.minimum_residual

This option is only used in case Mmax_small > 0. See Mmax_small for details.

Default: 1e-8

Definition at line 235 of file DetailedData.m.

NonlinEvol.DetailedData.epsilon_M_by_N_r = 1e-4

ratio between the stop epsilon criterion for collateral reduced basis spaces and reduced basis spaces.

This option is only used in case Mmax_small == 0. See Mmax_small for details.

Its purpose is to make the collateral reduced basis space more refined than the reduced basis space. This is necessary as the best possible error for the basis generation of the reduced basis space depends on the quality of the collateral reduced basis space.

Default: 1e-4

Definition at line 205 of file DetailedData.m.

NonlinEvol.DetailedData.extension_M_by_N_r = 4

sets the Greedy.Plugin.PODEI.M_by_N_ratio

This option is only used in case Mmax_small > 0. See Mmax_small for details.

Default: 4

Definition at line 247 of file DetailedData.m.

NonlinEvol.DetailedData.indicator_mode = "estimator"

string specifying which indicators shall be used by the error_indicators() method.

Default: "estimator"

Definition at line 289 of file DetailedData.m.

NonlinEvol.DetailedData.max_refinement_level = 5

sets the Greedy.TrainingSetAdaptation.max_refinement_level option

If this level is reached, the algorithm terminates and returns the generated reduced basis spaces.

Default: 5

Definition at line 124 of file DetailedData.m.

NonlinEvol.DetailedData.maximum_temporary_error_growth_factor = 0

maximum factor between the current maximum indicator and the smallest maximum error indicator during previous extensions

See Greedy.Plugin.PODEI.indicate_bad_basis_extension() for details.

Default: 0

Definition at line 223 of file DetailedData.m.

NonlinEvol.DetailedData.Mmax_small = 10

sets the Greedy.Plugin.PODEI.Mmax_small member

In order to use the estimator of a nonlinear evolution equation for a basis extension with a greedy search in the parameter space, a collateral reduced basis space for all existing operators needs to be present. For this reason at the beginning of the basis generation algorithm, a collateral reduced bases of size at most Mmax_small is generated

It uses an an Greedy.Plugin.EI instance with training set of size small_train_num_intervals as extension algorithm for a Greedy.Algorithm instance. The Greedy.Algorithm.stop_epsilon limit is set to ei_epsilon_small.

If Mmax_small is equal to 0, the initial collateral reduced bases are generated with stopping parameters stop_Mmax and stop_epsilon * epsilon_M_by_N_r, and the PODGreedyAlgorithm afterwards only extends the reduced basis space.

Default: 10

Definition at line 180 of file DetailedData.m.

NonlinEvol.DetailedData.noof_ei_extensions = 1

sets the number of ei extensions

See Greedy.Plugin.EI.noof_ei_extensions for details.

Default: 1

Definition at line 325 of file DetailedData.m.

NonlinEvol.DetailedData.refinement_mode = "adaptive"

sets the Greedy.TrainingSetAdaptation.refinement_mode option

Possible values are

uniform: the parameter sampling is refined uniformly
adaptive: the parameter sampling is refined adaptively, such that only regions of the parameter space with high estimated errors are refined.
none: no Greedy.TrainingSetAdaptation object is created

Default: "adaptive"

Definition at line 108 of file DetailedData.m.

NonlinEvol.DetailedData.refinement_theta = 0.2

sets the Greedy.TrainingSetAdaptation.refinement_theta option

This value \(\theta\) is multiplied by the number of leaf elements in the current parameter grid in order to compute the number grid cells to be refined.

Default: 0.5

Default: 0.2

Definition at line 135 of file DetailedData.m.

NonlinEvol.DetailedData.small_train_num_intervals = 2

number of intervals in the ParameterSampling.Uniform for the small training set \(M_{\text{small}}\) for the generation of an initial collateral reduced basis space.

See Mmax_small for details.

Default: 2

Definition at line 167 of file DetailedData.m.

NonlinEvol.DetailedData.stop_epsilon = 1e-5

sets the Greedy.Algorithm.stop_epsilon option

Default: 1e-5

Definition at line 298 of file DetailedData.m.

NonlinEvol.DetailedData.stop_max_val_train_ratio = 1.2

sets the Greedy.Algorithm.stop_max_val_train_ratio option

Default: 1.2

Definition at line 307 of file DetailedData.m.

NonlinEvol.DetailedData.stop_Mmax = 200

sets the Greedy.Plugin.EI.stop_Mmax option

Default: 200

Definition at line 271 of file DetailedData.m.

NonlinEvol.DetailedData.stop_Nmax = 50

sets the Greedy.Plugin.PODEI.stop_Nmax option

Default: 50

Definition at line 280 of file DetailedData.m.

NonlinEvol.DetailedData.stop_timeout = 12*60*60

sets the Greedy.Algorithm.stop_timeout option

Default: 12*60*60

Definition at line 316 of file DetailedData.m.

NonlinEvol.DetailedData.train_num_intervals = 3

number of intervals in the ParameterSampling.Uniform respectively number of vectors in the ParameterSampling.Random for the training set \(M_{\text{train}}\) of the parameter space \({\cal M}\).

Default: 3

Definition at line 86 of file DetailedData.m.

NonlinEvol.DetailedData.train_sample_mode = "uniform"

flag indicating whether the parameter sampling for the training set \(M_{\text{train}}\) type.

Possible values

uniform: (default) for a ParameterSampling.Uniform
random: for a ParameterSampling.Random

Default: "uniform"

Definition at line 72 of file DetailedData.m.

NonlinEvol.DetailedData.train_seed = 4321

If train_sample_mode == random, a ParameterSampling.Random is generated for the training set \(M_{\text{val}}\) with size train_num_intervals and seed train_seed.

Default: 4321

Definition at line 97 of file DetailedData.m.

NonlinEvol.DetailedData.val_seed = 1234

If the value of val_size is non-zero, a ParameterSampling.Random is generated for the validation set \(M_{\text{val}}\) with size val_size and seed val_seed.

Default: 1234

Definition at line 156 of file DetailedData.m.

NonlinEvol.DetailedData.val_size = 10

If this value is non-zero, a ParameterSampling.Random is generated for the validation set \(M_{\text{val}}\) with size val_size and seed val_seed.

Default: 10

Definition at line 146 of file DetailedData.m.

The documentation for this class was generated from the following file:

rbasis/problem_types/+NonlinEvol/DetailedData.m

Detailed Description

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation