Symmetric Relations

[Krishna Shrinivas]

Hey ,

I have this data set with four inputs and two outputs. Let the inputs be x1,x2,x3,x4 and the outputs, y1 and y2. Now  I am using Eureqa to model
y1 and y2 as functions of x1,x2,x3 and x4.

I have an important constraint, though , for my final models. I need them to be symmetric about (x1,x2) and (x3,x4) , i.e. ,Let the initial models be y1 = f1(x1,x2,x3,x4) and y2 = f2(x1,x2,x3,x4). Then   I would require y1 = f2(x3,x4,x1,x2) and y2 = f1(x3,x4,x1,x2). How I am attempting this right now is by actually doubling my dataset and flipping the points. Then for this dataset, I seek to find a general model. But it has not produced great results. Any tweaks or method?

Thanks in advance,
Krishna

[Michael Schmidt]

You could avoid duplicating rows in the data by using a more complex Target Expression. For example, you could enter:

max(abs(y1 - f(x1,x2,x3,x4)), abs(y1 - f(x2,x1,x4,x3))) = 0

This will minimize the absolute error for each symmetry case, which ever is worse. Then repeat this in another search using y2. I think using the max here helps avoid preference to one symmetry over the other while fitting and may help improve your results. But the symmetry maybe be a pretty restrictive constraint, let me know how it goes.

Michael

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