Surrogate Reference

Surrogates Properties

Auto Compute

When activated, all the defined surrogates are computed automatically at the end of the study run.

Surrogates Right-Click Actions

New Surrogate

Adds a new surrogate to the design study. One surrogate covers one response. Hence, if you want to have surrogates for all responses in a design study, you add a surrogate for each response.

Edit Surrogates

Opens a Surrogate Table displaying key data of the surrogates and allowing multiple editing of all the defined surrogates. An example table is shown below:

When hovering on any RMSE, Cross V or PRESS cell, the value is shown as percentages of the min, max, mean of the predicted response values computed through the surrogate.

Compute All

Computes all the defined surrogates with the latest settings. Usually required when surrogate settings are modified after the initial computation. If simulations for individual designs are not available, Design Manager reruns those simulations.

Cross Validate All

Performs a cross validation for all the computed surrogates using the Cross Validation settings defined in each surrogate.

Export to FMU...

Exports all the computed surrogates within this design study to an FMU file.

[surrogate] Properties

Each surrogate has the following properties:

Surrogate Type

Specifies the surrogate modeling approach used for the surrogate calculation. Each approach activates the corresponding sub-node with its properties.

Surrogate Type	Sub-node	Property	Setting
Kriging (default) Kriging is a method of interpolation which is based on statistical correlation between data sets (response values from executed design runs). It predicts the value of a function at a given point by computing a weighted average of the known values of the function in the neighborhood of the point.	Kriging	Function Type Specifies the fitting function type.	Gaussian Exponential Linear Spherical
		Regression Order Specifies the polynomial order within the range [0, 2].	Its default value is 1.
		Tuning Type Allows auto tuning of the Shape Factor in the Kriging model.	None Turns off automatic tuning. The Shape Factor must be adjusted manually to achieve the best fit. Fast Kriging Sweeps a fixed series of Shape Factors. In each sweep the same factor is applied all the data points. After completing the sweep procedure, the best Shape Factor is registered. This option mostly gives good cross-validation values but not necessarily the best possible ones. You may also be able to improve the cross-validation value by manually adjusting the Shape Factor in the neighborhood of the auto-tuned value Precise Kriging Uses an advanced optimization method that varies theta intervals for each data point. This option provides better tuning results than the Fast Kriging, but with greater computational expense. Gaussian Process Adds an additional noise factor to the fitting procedure. For this option, Design Manager automatically optimizes the fitting with the Shape Factors coming from the best results of the Kriging objective. Here, no manual shape modification is possible.
		Shape Factor Controls how much each data point affects the fitting surface. Small values smooth influence of single points, while large values enhance that influence.	The range of the shape factor is [1e-3, 50.0]. You can only set the value when Tuning Type is set to None.
Least Squares Least Squares model is a regression model that forms a best-fit polynomial of the known data set.	Least Squares	Function Type	Linear Quadratic
Radial Basis Function Radial Basis Function surrogates interpolate data points—the surrogates pass exactly through the response values. If the underlying behavior is smooth and there are enough data points to follow the shape, RBF surfaces can accurately represent complex data.	Radial Basis Function	Function Type	Gaussian Multi-Quadratic Inverse Multi-Quadratic Linear Cubic Thin Plate Spline
		Shape Factor Controls how much each data point affects the fitting surface. Small values smooth influence of single points, while large values enhance that influence.

Response

Specifies the study response for which the surrogate is computed.

Design Set

Specifies the set of design runs selected for the computing surrogate. By default, [All] design runs are selected.

Cross Validation Scheme

Specifies the cross validation scheme with which the predictive accuracy of surrogate is estimated. Each scheme defines a methodology by which it divides the original data set into a validation set and a training set (the remaining data from the data set after excluding the validation data). The available schemes are:

• K-Fold

  This scheme divides the known data set into k sub-samples. Each sub-sample is used once as validation data to validate the remaining k-1 sub-samples. The validation procedure repeats k times. The K-Fold scheme is efficient when the data set is large.

• Leave-one-out

  This scheme selects one data point as the validation set to validate all the remaining data. The validation procedure repeats m times where m is the dimension of the collected data set. The Leave-one-out scheme is efficient when the data set is small. No further validation settings are required for this scheme.

Cross Validation K-Fold Value

Specifies K-Fold value for K-Fold cross validiation scheme—number of samples to include in each sub-sample for the validation with the range [2, (number of designs in the selected Design Set or 10, which ever is greater)]. The default setting is 10.

Cross Validation Seed

Sets the seed for random number generation during K-Fold Cross Validation.

Correlation Coefficient (R2) (read-only)

After computation, displays the correlation coefficient between the original values and the predicted values of the training data sets.

Adjusted Correlation Coefficient (R2adj) (read-only)

Displays the correlation coefficient adjusted for the number of terms in the regression model. Only applicable for the surrogate type Least Squares.

Root Mean Squared Error (RMSE) (read-only)

Displays the root mean square error of the predicted values towards the original values of the training data sets. This value has the same unit as the study response for which the surrogate is calculated.

Cross V (read-only)

Displays the Root Mean Squared Error (RMSE) of the Cross V(alidation) residuals of all the designs from the specified Design Set (All by default) as shown in [eqnlink].

The Cross V(alidation) residual of a design is the difference between the actual response value and the response value predicted by the reduced surrogate fit according to the cross-validation scheme specified. The value has the same unit as the study response for which the surrogate is calculated.

PRESS (read-only)

Displays the Root Mean Squared Error (RMSE) of the PRESS residuals of all the designs from the specified Design Set (All by default).

To compute the PRESS residual of a design, this design is firstly removed from the surrogate calculation. Afterwards, the response value is predicted using the reduced surrogate fit. The difference between the actual response value and the predicted value is the PRESS residual of this design. It has the same unit as the study response for which the surrogate is calculated. When Leave-one-out is selected as cross-validation scheme, the PRESS residuals of one design are identical to the Cross V(alidation) residuals.

[surrogate] Right-click Actions

Compute

Computes the selected surrogate with the latest settings.

Cross Validate

Performs a cross validation for the selected surrogate using the Cross Validation settings defined.

Open Residual Table

Opens the residual table of the selected surrogate showing the following parameters for each design run individually:

• Actual response values from each design run
• Predicted response values calculated by the surrogate
• Residual
• Cross V(alidation) Residuals: The Cross V(alidation) residual of a design is the difference between the actual response value and the response value predicted by the reduced surrogate fit according to the cross-validation scheme specified.
• PRESS Residuals: To compute the PRESS residual of a design, this design is firstly removed from the surrogate calculation. Afterwards, the response value is predicted using the reduced surrogate fit. The difference between the actual response value and the predicted value is the PRESS residual of this design.

An example is shown below:

Export to FMU...

Exports the selected surrogate to an FMU file. The exported FMU file has following properties:

• The exported FMU has the type of Model Exchange with the FMI (functional Mock-up Interface) version 2.0.
• The import and running of the exported FMU do not require license of the original tool. See also Surrogate Licensing.
• When surrogates share the same input parameters, you can export multiple surrogates into one FMU file by multi-selecting them before export.

Export to File...

Exports the selected surrogate to an external file with one of the following code formats:

• Fortran 90 Code Files (*.f90)
• Java Code Files (*.java)
• Python Code Files (*.py)
• MATLAB M- Files (*.m)
• Visual Basic for Application Code File (*.bas)

This action is disabled when multiple surrogates are selected.

Create Plot

Creates one of the following plot types for the selected surrogate:

• Surrogate—Surrogate Fit
• Surrogate—Actual vs Residual