1Blurb::
2Select a surrogate model with global support
3Description::
4The global surrogate model requires specification of one of the
5following approximation types:
6<ol>
7  <li> Polynomial </li>
8  <li> Gaussian process (Kriging interpolation) </li>
9  <li> Layered perceptron artificial neural network approximation </li>
10  <li> MARS </li>
11  <li> Moving least squares </li>
12  <li> Radial basis function
13  <li> Voronoi Piecewise Surrogate (VPS)
14</ol>
15All these approximations are implemented
16in SurfPack \cite Giunta2006, except for VPS. In addition, a second version of
17Gaussian process is implemented directly in %Dakota.
18
19<b> Training Data </b>
20
21Training data can be taken from prior runs, stored in a datafile,
22or by running a Design of Experiments method. The keywords listed
23below are used to determine how to collect training data:
24\li \c dace_method_pointer
25\li \c reuse_points
26\li \c import_points_file
27\li \c use_derivatives
28The source of training data
29is determined by the contents of a provided \c import_points_file,
30whether \c reuse_points and \c use_derivatives are specified,
31and the contents of the method block specified by \c dace_method_pointer.
32\c use_derivatives is a special case, the other keywords are discussed below.
33
34The number of training data points used in building a global approximation is
35determined by specifying one of three point counts:
36
37<ol>
38  <li> \c minimum_points: minimum required or minimum "reasonable"
39       amount of training data. Defaults to d+1 for d input dimensions
40       for most models, e.g., polynomials override to the number of
41       coefficients required to estimate the requested order.</li>
42
43  <li> \c recommended_points: recommended number of training data,
44       (this is the default option, if none of the keywords is
45       specified).  Defaults to 5*d, except for polynomials where it's
46       equal to the minimum.</li>
47
48  <li> \c total_points: specify the number of training data points.
49     However, if the \c total_points value is less than the default
50     \c minimum_points value, the \c minimum_points value is used. </li>
51</ol>
52
53The sources of training data depend on the number of training points,
54\f$ N_{tp} \f$, the number of points in the import file, \f$ N_{if} \f$,
55and the value of \c reuse_points.
56<ul>
57<li> If there is no import file, all training data come from the DACE method </li>
58<li> If there is an import file, all \f$ N_{if} \f$ points from the file are used,
59  and the remaining \f$ N_{tp} - N_{if} \f$ points come from the DACE method </li>
60<li> If there is an import file and \c reuse_points is:
61  <ul>
62  <li> \c none - all \f$ N_{tp} \f$ points from DACE method
63  </li>
64  <li> \c region - only the points within a trust region are taken from the
65    import file, and all remaining points are from the DACE method.
66  </li>
67  <li> \c all - (Default) all \f$ N_{if} \f$ points from the file are used,
68  and the remaining \f$ N_{tp} - N_{if} \f$ points come from the DACE method
69  </li>
70  </ul>
71</li>
72</ul>
73
74
75<b> Surrogate Correction </b>
76
77A \c correction model can be added to the constructed surrogate in
78order to better match the training data. The specified correction method will be applied to the surrogate, and then the corrected
79surrogate model is used by the method.
80
81Finally, the quality of the surrogate can be tested using the
82\c metrics and \c challenge_points_file keywords.
83
84Topics::
85Examples::
86Theory::
87Global methods, also referred to as response surface methods,
88involve many points spread over the parameter ranges of interest.
89These surface fitting methods work in conjunction with the sampling
90methods and design of experiments methods.
91
92
93<b> Procedures for Surface Fitting </b>
94
95The surface fitting process consists of three steps:
96<ol>
97  <li> selection of a set of design points
98  </li>
99  <li> evaluation of the true response quantities
100  (e.g., from a user-supplied simulation code) at these design points,
101  </li>
102  <li> using the response data to solve for the unknown coefficients
103  (e.g., polynomial coefficients, neural network weights, kriging
104  correlation factors) in the surface fit model.
105  </li>
106</ol>
107In cases where there is
108more than one response quantity (e.g., an objective function plus one
109or more constraints), then a separate surface is built for each
110response quantity. Currently, the surface fit models are built using
111only 0\f$^{\mathrm{th}}\f$-order information (function values only), although
112extensions to using higher-order information (gradients and Hessians)
113are possible.
114
115Each surface fitting method employs a different
116numerical method for computing its internal coefficients. For example,
117the polynomial surface uses a least-squares approach that employs a
118singular value decomposition to compute the polynomial coefficients,
119whereas the kriging surface uses Maximum Likelihood Estimation to
120compute its correlation coefficients. More information on the
121numerical methods used in the surface fitting codes is provided in the
122Dakota Developers Manual.
123
124
125Faq::
126See_Also::	model-surrogate-local, model-surrogate-hierarchical, model-surrogate-multipoint
127