.. _model-surrogate-global-radial_basis:

""""""""""""
radial_basis
""""""""""""


Radial basis function (RBF) model


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

   model-surrogate-global-radial_basis-bases
   model-surrogate-global-radial_basis-max_pts
   model-surrogate-global-radial_basis-min_partition
   model-surrogate-global-radial_basis-max_subsets
   model-surrogate-global-radial_basis-export_model
   model-surrogate-global-radial_basis-import_model


**Specification**

- *Alias:* None

- *Arguments:* None


**Child Keywords:**

+-------------------------+--------------------+--------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword     | Dakota Keyword Description                    |
|                         | Group              |                    |                                               |
+=========================+====================+====================+===============================================+
| Optional                                     | `bases`__          | Initial number of radial basis functions      |
+----------------------------------------------+--------------------+-----------------------------------------------+
| Optional                                     | `max_pts`__        | Maximum number of RBF CVT points              |
+----------------------------------------------+--------------------+-----------------------------------------------+
| Optional                                     | `min_partition`__  | (Inactive) Minimum RBF partition              |
+----------------------------------------------+--------------------+-----------------------------------------------+
| Optional                                     | `max_subsets`__    | Number of trial RBF subsets                   |
+----------------------------------------------+--------------------+-----------------------------------------------+
| Optional                                     | `export_model`__   | Exports surrogate model in user-specified     |
|                                              |                    | format(s)                                     |
+----------------------------------------------+--------------------+-----------------------------------------------+
| Optional                                     | `import_model`__   | Import surrogate model from archive file      |
+----------------------------------------------+--------------------+-----------------------------------------------+

.. __: model-surrogate-global-radial_basis-bases.html
__ model-surrogate-global-radial_basis-max_pts.html
__ model-surrogate-global-radial_basis-min_partition.html
__ model-surrogate-global-radial_basis-max_subsets.html
__ model-surrogate-global-radial_basis-export_model.html
__ model-surrogate-global-radial_basis-import_model.html



**Description**


Radial basis functions :math:`\phi`  are functions whose value typically
depends on the distance from a center point, called the centroid,
:math:`{\bf c}` .

The surrogate model approximation comprises a sum of K weighted radial
basis functions:

.. math::  \hat{f}({\bf x})=\sum_{k=1}^{K}w_{k}\phi({\parallel {\bf x} - {\bf c_{k}} \parallel}) 

These basis functions take many forms, but Gaussian kernels or splines
are most common.  The Dakota implementation uses a Gaussian radial
basis function.  The weights are determined via a linear least squares
solution approach.  See :cite:p:`Orr96` for more details.

*Known Issue: When using discrete variables, there have been
sometimes significant differences in surrogate behavior observed
across computing platforms in some cases.  The cause has not yet been
fully diagnosed and is currently under investigation.  In addition,
guidance on appropriate construction and use of surrogates with
discrete variables is under development.  In the meantime, users
should therefore be aware that there is a risk of inaccurate results
when using surrogates with discrete variables.*


