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		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

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:

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

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 [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.