Kriging? What is Kriging or who is Kriging?

If you opened this post with these questions in mind, I am very happy that I got someone new, curious about Kriging.

Kriging is  one of the various techniques available in Isight to create surrogate models . This technique is especially suitable to approximate highly non-linear functions, like shown below. The left image shows the function, middle the  actual contour and the right showing the kriging approximation of the function.

 Alrite, I know what Kriging is. But when I use it, I dont get a good approximation. And increasing the sampling points doesnt seem to improve the approximation.  Is this what you say?  Read further...

Kriging requires the sample points to be :

1. Evenly spread over the design space.

2. Not too many.

Optimal Latin Hypercube(OLH)  sampling method generates sampling points using Latin Hypercube technique and optimizes the point positions to be spread evenly over the design space. This sampling method is recommended for Kriging approximation.

So how many is too many? There is no real quantifiable number here.  Try to have points less than 500, the fewer the better.

In general if you have a complex multimodal function, Kriging will do a good job if you choose OLH sampling and the number of sampling points are about 100. Anything beyond that you will have to do actual comparisions with other approximation methods like Radial Basis Functions or Elliptical Basis Functions