Package Greedy

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Detailed Description

Customizable implementation of an abstract greedy algorithm.

Implementations

The default implementation of a greedy basis generation algorithm is implemented by GreedyBasisGeneration. Depending on the extension object used to initialize a GreedyBasisGeneration object, it can produce

• a reduced basis for reduced simulations,
• a (collateral) reduced basis for empirical interpolation of parametrized operators or functions or
• a combination of the above.

See Greedy.Plugin for a detailed description of the possible extension classes.

The default greedy basis generation algorithm can be extended in a modular way by (Meta-) basis generation classes.

(Meta-) basis generation classes

(Meta-) basis generation can be used to refine the generation of the reduced bases or combine several generation algorithms in a generic way.

At the moment the following Meta classes are implemented:

• ParameterSpaceAdaptation refines the parameter training set used by the GreedyBasisGeneration each time the generation stopped a 'stopped_on_max_val_train_ratio' message.
• CombinedBasisGeneration can be used to combine
  • two empirical interpolation generation algorithms or
  • one generation algorithm producing reduced bases for empirical interpolation and one reduced basis generation algorithm. In this case the result can be used for reduced simulations depending on empirical operator interpolation, like e.g. implemented in the NonlinEvol.ReducedModel.

Detailed data container

Greedy.Interface implementations usually store their generated reduced bases in a tree-like data structure fulfilling the Greedy.DataTree.Detailed.INode interface. All nodes have information properties which can be changed by the methods defined in Greedy.DataTree.Info.

Example usage (Quickstart)

In order to create a reduced basis one first needs to obtain a model structure and a suitable ReducedModel, e.g. for a linear evolution model

  model_descr     = convdiff_model();
  [dmodel,rmodel] = gen_models(model_descr);

Afterwards, one needs to specify the extension algorithm, in this case it is a standard rb extension algorithm

  rb_gen    = SnapshotsGenerator.Trajectories(dmodel);
  rb_plugin = Greedy.Plugin.POD(rb_gen);

The first line of the previous code block instantiates a SnapshotsGenerator.Trajectories object which is used to initiate the detailed simulations and cache their results on the harddrive. See SnapshotsGenerator for more details on this topic.

Now, we can instantiate the reduced basis generation algorithm after specifying the training parameter set, an optional validation parameter set, and adjusting the termination condition for the maximum error indicator.

  M_train = ParameterSampling.Uniform(5);        % 5 grid cells in each dimension
  M_val   = ParameterSampling.Random(10, 12345); % 10 randomly chosen parameters with random seed '12345'

  pod_greedy = Greedy.Algorithm(rb_ext, M_train, M_val);
  pod_greedy.stop_epsilon = 1e-4;

In the end, the basis generation can then be started by

  detailed_data = gen_detailed_data(pod_greedy);

Of course the above code is executed automatically by the LinEvol.DetailedData class. Some parts of the created basis generation object can be controlled by options defined by a BasisGenDescr structure as a second argument to gen_default_models().

Packages
package	DataTree
	DataTree implementation for generated detailed and reduced data
package	Info
	Information objects generated throught Greedy execution.
package	Plugin
	Specialization plugins for the greedy algorithm.
package	User
	Interface classes to be implemented by the Greedy.Algorithm user.
Classes
class	Algorithm
	default greedy basis generation class More...
class	Checkpoint
	Helper class used to store and restore data tree objects at specified checkpoints. More...
class	Combined
	combines two or more instances of a Greedy.Interface class by executing them subsequently. More...
class	EiTpart
class	Interface
	Interface class for all kind of reduced basis generation algorithms More...
class	MetaInterface
class	TrainingSetAdaptation
	greedy basis generation extension which adaptively refines the trainings parameter set. More...