Creating an Approximation Using the Universal Kriging Model

From the Approximations table on the left side of the Predict page, select

.

Note: If no approximations have been created, you can also click Create New Approximation.

The Create New Approximation dialog box appears.

From the Algorithm tab, enter a name for the approximation model.

From the Approximation Type menu, select Universal Kriging.

Note: If desired, you can create approximations using more than one model and compare the approximations side-by-side or in an overlay plot to determine which model produced the best numerical solution.

Enter a value for the smoothing parameter, Alpha (0 ≤ alpha ≤ 0.1).

Results Analytics uses the value of Alpha to relax the requirement that the Universal Kriging model approximation pass through every single data point. All points that are closer than the value of Alpha are removed from the sample set before fitting. By not going through every point, Results Analytics can effectively smooth noisy functions and provide an approximation that may be easier to optimize. Enter a value of zero to stop the conditioning of the matrix.

Select the Correlation Function. The correlation functions interpolate the data points exactly.

The following options are available:

Option	Description
Gaussian (default)	Use the Gaussian correlation function for approximating smooth functions. However, it produces a poor fit when sampling points are too close.
Exponential	Use the Exponential correlation function if the sample points are close.
Cubic Spline	Use the Cubic Spline correlation function to correlate data that does follow a specific pattern. The Cubic Spline correlation function is more accurate than linear interpolation and provides a smooth interpolant.
Matern Linear	Use the Matern Linear correlation function if the Gaussian and Matern Cubic correlation functions produced an unacceptable fit. The Matern Linear correlation is more robust, but less accurate, than the Matern Cubic correlation function.
Matern Cubic	Use the Matern Cubic correlation function if the Gaussian correlation function produced an unacceptable fit. Typically, the Matern Cubic correlation function is more accurate than the Matern Linear correlation function.

Enter a value for the Minimum distance between points.

Occasionally, when points are clustered together the matrices used in fitting the Kriging model become ill-conditioned resulting in a poor fit. You can filter points from the sample based on distance to avoid a poor fit. All points that are closer than the Minimum distance between points are removed from the sample set before fitting. Results Analytics uses other numerical techniques internally to improve the performance and robustness of the approximation.

Select Maximum Likelihood Estimate for the Optimize On technique to control how the best

θ_{k}

values are calculated.

Results Analytics performs a sampling of $θ$ values and chooses the best $θ$ for every output parameter by maximizing the likelihood of obtaining the observed data.

Select the Input Parameter Scaling to specify the method used to standardize the range of the input parameters.

Option	Description
Min-Max Normalization (default)	Normalize the input parameter values between zero and one.
Mean Zero Standardization	Rescale the input parameter values to a mean of zero with unit variance.

From the Datasets tab, select datasets to exclude from approximation generation.

From the Inputs tab, select input parameters to exclude from the generation of a specific approximation.

These inputs will not be used in training and will not be displayed in the prediction profiler.

From the Validation tab, set the validation type and validation hyperparameters such as Number of Folds for K-Folds Cross Validation.

Click Create to create the approximation.

The approximation is created with the name you specified and appears in the list of approximations.