Dakota Reference Manual  Version 6.0
Large-Scale Engineering Optimization and Uncertainty Analysis
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global


Select a surrogate model with global support

Specification

Alias: none

Argument(s): none

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Required
(Choose One)
Group 1 gaussian_process Use a Gaussian Process surrogate
mars Multivariate Adaptive Regression Spline (MARS)
moving_least_squares Moving Least Squares surrogate models
neural_network Artificial Neural Network Models
radial_basis Radial Basis Functions
polynomial Linear, Quadratic, or Cubic Polynomial Models
Optional
(Choose One)
Group 2 total_points Specify the number of training points
minimum_points Construct surrogate with the minimum amount of points
recommended_points (Default) Construct surrogate with the recommended amount of points
Optional dace_method_pointer Specify a method to gather training data
Optional reuse_points Specify how to use existing training data
Optional import_points_file Specify file containing points (variable and response values)
Optional export_points_file Specify file to write out the responses from the surrogate
Optional use_derivatives Use derivative data to construct surrogate models
Optional correction Correction approaches for surrogate models
Optional metrics Compute metrics of surrogate quality
Optional challenge_points_file Specify a datafile of points to compare surrogate responses against

Description

The global surrogate model requires specification of one of the following approximation types:

  1. Polynomial
  2. Gaussian process (Kriging interpolation)
  3. Layered perceptron artificial neural network approximation
  4. MARS
  5. Moving least squares
  6. Radial basis function

All these approximations are implemented in SurfPack[34]. 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 provided import_points_file, whether reuse_points and use_derivatives are specified, and the contents of the method block specified by dace_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:

  1. minimum_points: minimum "reasonable" amount of training data, based on Dakota's heuristics
  2. recommended_points: recommended number of training data, based on Dakota's heuristics (this is the default, if none of the keywords is specified)
  3. total_points: specify the number of training data points. However, if the total_points value is less than the default minimum_points value, the minimum_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 method
    • region - 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:

  1. selection of a set of design points
  2. evaluation of the true response quantities (e.g., from a user-supplied simulation code) at these design points,
  3. 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 higher-order 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 least-squares 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.

See Also

These keywords may also be of interest: