.. _method-multilevel_sampling-weighted-search_model_graphs:

"""""""""""""""""""
search_model_graphs
"""""""""""""""""""


For weighted multilevel Monte Carlo, this option activates a search over possible hierarchical model graphs



.. toctree::
   :hidden:
   :maxdepth: 1

   method-multilevel_sampling-weighted-search_model_graphs-model_selection
   method-multilevel_sampling-weighted-search_model_graphs-no_recursion
   method-multilevel_sampling-weighted-search_model_graphs-full_recursion


**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* NO_GRAPH_RECURSION


**Child Keywords:**

+-------------------------+--------------------+---------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword      | Dakota Keyword Description                    |
|                         | Group              |                     |                                               |
+=========================+====================+=====================+===============================================+
| Optional                                     | `model_selection`__ | Perform a recursion of admissible model       |
|                                              |                     | subsets for a given model ensemble            |
+-------------------------+--------------------+---------------------+-----------------------------------------------+
| Required (Choose One)   | DAG Ensemble       | `no_recursion`__    | Do not recur over admissible DAGs for a given |
|                         | Generation Option  |                     | model ensemble                                |
|                         |                    +---------------------+-----------------------------------------------+
|                         |                    | `full_recursion`__  | Perform a full recursion of all admissible    |
|                         |                    |                     | DAGs for a given model ensemble               |
+-------------------------+--------------------+---------------------+-----------------------------------------------+

.. __: method-multilevel_sampling-weighted-search_model_graphs-model_selection.html
__ method-multilevel_sampling-weighted-search_model_graphs-no_recursion.html
__ method-multilevel_sampling-weighted-search_model_graphs-full_recursion.html



**Description**


Referring to :dakkw:`method-approximate_control_variate-acv_recursive_diff`,
weighted MLMC is a special case of ACV-RD, resulting in a forward to
the generalized ACV solver for the case of a fixed hierarchical DAG.

While the use of a hierarchical DAG is required in MLMC, the approximation
selections and orderings within this DAG can be varied, so generalized
ACV capabilities for model graph search (see
:dakkw:`method-multilevel_sampling-weighted-search_model_graphs-full_recursion`)
and model selection (see
:dakkw:`method-multilevel_sampling-weighted-search_model_graphs-model_selection`)
are available.





**Examples**


Note that the default for weighted MLMC is no search,

.. code-block::

    method,
        multilevel_sampling
	  pilot_samples = 20 seed = 1237
	  weighted
	  max_function_evaluations = 500

with options to activate search over model ordering,

.. code-block::

    method,
        multilevel_sampling
	  pilot_samples = 20 seed = 1237
	  weighted
	    search_model_graphs full_recursion
	  max_function_evaluations = 500

over model subset selection,

.. code-block::

    method,
        multilevel_sampling
	  pilot_samples = 20 seed = 1237
	  weighted
	    search_model_graphs no_recursion model_selection
	  max_function_evaluations = 500

or over both.

.. code-block::

    method,
        multilevel_sampling
	  pilot_samples = 20 seed = 1237
	  weighted
	    search_model_graphs full_recursion model_selection
	  max_function_evaluations = 500