.. _method-multilevel_polynomial_chaos-discrepancy_emulation:

"""""""""""""""""""""
discrepancy_emulation
"""""""""""""""""""""


Formulation for emulation of model discrepancies.


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

   method-multilevel_polynomial_chaos-discrepancy_emulation-distinct
   method-multilevel_polynomial_chaos-discrepancy_emulation-recursive


**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* distinct


**Child Keywords:**

+-------------------------+--------------------+--------------------+---------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword     | Dakota Keyword Description                  |
|                         | Group              |                    |                                             |
+=========================+====================+====================+=============================================+
| Required (Choose One)   | Discrepancy        | `distinct`__       | Distinct formulation for emulation of model |
|                         | Emulation Approach |                    | discrepancies.                              |
|                         |                    +--------------------+---------------------------------------------+
|                         |                    | `recursive`__      | Recursive formulation for emulation of      |
|                         |                    |                    | model discrepancies.                        |
+-------------------------+--------------------+--------------------+---------------------------------------------+

.. __: method-multilevel_polynomial_chaos-discrepancy_emulation-distinct.html
__ method-multilevel_polynomial_chaos-discrepancy_emulation-recursive.html



**Description**


In many uncertainty quantification approaches, model discrepancies are
emulated using, e.g., polynomial chaos, stochastic collocation, or
Gaussian process models.  Two formulations are available for this
emulation:


1. ``distinct`` emulation (default), in which we directly approximate the difference or ratio between the evaluations of two models or solution levels.

2. ``recursive`` emulation (experimental option), in which we approximate a difference or ratio among the new model evaluation and the emulator approximation of the previous model.


The latter approach is a form of hierarchical emulation in which we
emulate the surplus between the previous emulator and the new modeling
level.  This approach has a few advantages: (i) it reduces bias by
correcting for emulation errors that occur at previous levels, and (ii)
it does not require paired model evaluations for each discrepancy level,
which reduces cost, allows for disparate sample points, and simplifies
data imports.

On the other hand, its primary disadvantage is that the aggregate
emulation is only as good as its weakest link, in that a poor emulator
recovery can create difficulty in accurately resolving discrepancies
that are recursively dependent on it.  Thus, the ``distinct`` approach
may tend to be more expensive in exchange for greater robustness.



**Examples**



.. code-block::

    method,
            multilevel_polynomial_chaos
       expansion_order_sequence = 2
       collocation_ratio = .9
       orthogonal_matching_pursuit
       discrepancy_emulation recursive