How do I determine the best neural network architecture for a problem with 3 inputs and 12 outputs?

Question

This post continues the topic in the following post: Is it possible to train a neural network with 3 inputs and 12 outputs?.

I conducted several experiments in MATLAB and selected those neural networks that best approximate the data.

Here is a list of them:

• Cascade-forward backpropagation

• Elman backpropagation

• Generalized regression

• Radial basis (exact fit)

I did not notice a fundamental difference in quality, except for Elman's backpropagation, which had a higher error than the rest.

How to justify the choice of the structure of the neural network in this case?