HyperKriging

HyperKriging is a scheme used to create predictive models with data sets coming from deterministic computer simulations, an area of application commonly known as the Design and Analysis of Computer Experiments (DACE). These experiments are unique because they do not require some concepts such as replication. This approximation method is designed to tightly pass through and smoothly interpolate between the known points.

Usability Characteristics

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HyperKriging tries to go through the exact sampling points, and in general, the residuals are small, if not zero. As a result, diagnostic measures using only the complete input matrix do not produce meaningful values. Cross-validation results provide some diagnostics using a special scheme using only the input points. To get detailed diagnostics on the quality of a HyperKriging fit, it is suggested that you use a validation matrix.

•	Suitable for modeling highly nonlinear output response data that does not contain numerical noise.

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Applicability of HyperKriging and Radial Basis Function (RBF) methods are similar in terms of physics (they both are suggested for highly nonlinear output responses with no noise). It is suggested that you use HyperKriging for large studies that contain a large number of sampling points, whereas, RBF is suggested for studies with a large number of variables.

Note:

As a result, RBF Fits are evaluated faster than HyperKriging Fits when used in approaches.

The images below compares a quadratic polynomial model and a HyperKriging model for a function of a single variable.

leastsquaresquadreg

Least squares quadratic regression

krigingmodel

HyperKriging model