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	experimental_gaussian_process	Use the Gaussian process regression surrogate from the surrogates module
		gaussian_process	Gaussian Process surrogate model
		mars	Multivariate Adaptive Regression Spline (MARS)
		moving_least_squares	Moving Least Squares surrogate models
		function_train	Global surrogate model based on functional tensor train decomposition
		neural_network	Artificial neural network model
		radial_basis	Radial basis function (RBF) model
		polynomial	Polynomial surrogate model
		experimental_polynomial	Use a deterministic polynomial surrogate
Optional		domain_decomposition	Piecewise Domain Decomposition for Global Surrogate Models
Optional (Choose One)	Number of Build Points	total_points	Specified number of training points
		minimum_points	Construct surrogate with minimum number of points
		recommended_points	Construct surrogate with recommended number of points
Optional (Choose One)	Build Data Source	dace_method_pointer	Specify a method to gather training data
		truth_model_pointer	A surrogate model pointer that guides a method to whether it should use a surrogate model or compute truth function evaluations
Optional		reuse_points	Surrogate model training data reuse control
Optional		import_build_points_file	File containing points you wish to use to build a surrogate
Optional		export_approx_points_file	Output file for surrogate model value evaluations
Optional		use_derivatives	Use derivative data to construct surrogate models
Optional		correction	Correction approaches for surrogate models
Optional		metrics	Compute surrogate quality metrics
Optional		import_challenge_points_file	Datafile of points to assess surrogate quality

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

7. 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 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 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.

2. 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.

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.