Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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radial_basis


Radial basis function (RBF) model

Specification

Alias: none

Argument(s): none

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-selected format

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[67] for more details.