global
Select a surrogate model with global support
Specification
Alias: None
Arguments: None
Child Keywords:
Required/Optional 
Description of Group 
Dakota Keyword 
Dakota Keyword Description 

Required (Choose One) 
Global Surrogate Type 
Use the Gaussian process regression surrogate from the surrogates module 

Gaussian Process surrogate model 

Multivariate Adaptive Regression Spline (MARS) 

Moving Least Squares surrogate models 

Global surrogate model based on functional tensor train decomposition 

Artificial neural network model 

Radial basis function (RBF) model 

Polynomial surrogate model 

Use a deterministic polynomial surrogate 

Optional 
Piecewise Domain Decomposition for Global Surrogate Models 

Optional (Choose One) 
Number of Build Points 
Specified number of training points 

Construct surrogate with minimum number of points 

Construct surrogate with recommended number of points 

Optional (Choose One) 
Build Data Source 
Specify a method to gather training data 

A surrogate model pointer that guides a method to whether it should use a surrogate model or compute truth function evaluations 

Optional 
Surrogate model training data reuse control 

Optional 
File containing points you wish to use to build a surrogate 

Optional 
Output file for surrogate model value evaluations 

Optional 
Use derivative data to construct surrogate models 

Optional 
Correction approaches for surrogate models 

Optional 
Compute surrogate quality metrics 

Optional 
Datafile of points to assess surrogate quality 
Description
The global surrogate model requires specification of one of the following approximation types:
Polynomial
Gaussian process (Kriging interpolation)
Layered perceptron artificial neural network approximation
MARS
Moving least squares
Radial basis function
Voronoi Piecewise Surrogate (VPS)
All these approximations are implemented in SurfPack [GSB+06], except for VPS. In addition, a second version of Gaussian process is implemented directly in Dakota.
Training Data
Training data can be taken from prior runs, stored in a datafile, or by running a Design of Experiments method. The keywords listed below are used to determine how to collect training data:
dace_method_pointer
reuse_points
import_points_file
use_derivatives
The source of training data is determined by the contents of a providedimport_points_file
, whetherreuse_points
anduse_derivatives
are specified, and the contents of the method block specified bydace_method_pointer
.use_derivatives
is a special case, the other keywords are discussed below.
The number of training data points used in building a global approximation is determined by specifying one of three point counts:
minimum_points
: minimum required or minimum “reasonable” amount of training data. Defaults to d+1 for d input dimensions for most models, e.g., polynomials override to the number of coefficients required to estimate the requested order.recommended_points
: recommended number of training data, (this is the default option, if none of the keywords is specified). Defaults to 5*d, except for polynomials where it’s equal to the minimum.total_points
: specify the number of training data points. However, if thetotal_points
value is less than the defaultminimum_points
value, theminimum_points
value is used.
The sources of training data depend on the number of training points,
\(N_{tp}\) , the number of points in the import file, \(N_{if}\) ,
and the value of reuse_points
.
If there is no import file, all training data come from the DACE method
If there is an import file, all \(N_{if}\) points from the file are used, and the remaining \(N_{tp}  N_{if}\) points come from the DACE method
If there is an import file and
reuse_points
is:none
 all \(N_{tp}\) points from DACE methodregion
 only the points within a trust region are taken from the import file, and all remaining points are from the DACE method.all
 (Default) all \(N_{if}\) points from the file are used, and the remaining \(N_{tp}  N_{if}\) points come from the DACE method
Surrogate Correction
A correction
model can be added to the constructed surrogate in
order to better match the training data. The specified correction method will be applied to the surrogate, and then the corrected
surrogate model is used by the method.
Finally, the quality of the surrogate can be tested using the
metrics
and challenge_points_file
keywords.
Theory
Global methods, also referred to as response surface methods, involve many points spread over the parameter ranges of interest. These surface fitting methods work in conjunction with the sampling methods and design of experiments methods.
Procedures for Surface Fitting
The surface fitting process consists of three steps:
selection of a set of design points
evaluation of the true response quantities (e.g., from a usersupplied simulation code) at these design points,
using the response data to solve for the unknown coefficients (e.g., polynomial coefficients, neural network weights, kriging correlation factors) in the surface fit model.
In cases where there is more than one response quantity (e.g., an objective function plus one or more constraints), then a separate surface is built for each response quantity. Currently, the surface fit models are built using only 0 \(^{\mathrm{th}}\) order information (function values only), although extensions to using higherorder information (gradients and Hessians) are possible.
Each surface fitting method employs a different numerical method for computing its internal coefficients. For example, the polynomial surface uses a leastsquares approach that employs a singular value decomposition to compute the polynomial coefficients, whereas the kriging surface uses Maximum Likelihood Estimation to compute its correlation coefficients. More information on the numerical methods used in the surface fitting codes is provided in the Dakota Developers Manual.