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