# radial_basis

Radial basis function (RBF) model

**Specification**

*Alias:*None*Arguments:*None

**Child Keywords:**

Required/Optional |
Description of Group |
Dakota Keyword |
Dakota Keyword Description |
---|---|---|---|

Optional |
Initial number of radial basis functions |
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Optional |
Maximum number of RBF CVT points |
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Optional |
(Inactive) Minimum RBF partition |
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Optional |
Number of trial RBF subsets |
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Optional |
Exports surrogate model in user-specified format(s) |
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Optional |
Import surrogate model from archive file |

**Description**

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

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

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 [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.*