Advanced System - GRNN - Saddle

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Problem

This problem is designed to demonstrate the capability of General Regression Neural Networks (GRNN).  GRNN will be used to fit a surface through a number of points in 3 dimensional space.  We will be modeling the Saddle function, z=x^2 - y^2 (where x^2 means x squared).  The Saddle function is so named because its graph looks like a saddle.

 

Inputs and Outputs

There are two inputs, x and y, both ranging from -6 to +6. Our Pattern file contains 169 combinations of x and y with integer values.  After those, there are 20 patterns which do not have integer values which will be used for a test set.

 

We have used the Rules module to calculate z.  Load up Rules to see how that was done.

 

Processing

First a test set was created by extracting all patterns after the 169th one.  Then the GRNN training was completed with Calibration on, and we applied the new net to the pattern file.  Following that, we attached the output to the pattern file to create a new output (.out) file. You may print that to see how the network's z values (in the last column) compare to the actual ones.