Biological 'Black Box' - how to test for underlying logic?
There's a mathematics of neural networks you need to look into, and many other nonlinear techniques.  In short, you have a huge literature to catch up on.  You need to be much more specific about what you're trying to accomplish before you'll get any real help, but I suggest you look into the journal "Neural Networks" to help you start sorting this out.  It might help you to pick a field where such tools are often used, like the epilepsy literature, and look to see what applies to your field.

Generically, all the methodology you might choose to use comes under the heading "Computational Neuroscience".  The best general purpose intro I know of that will walk you through many types of models is Kristoff Koch's "Methods in Neuronal Modeling".  It's a hair dated, but should at least teach you a bit of the language of what you're trying.  Another possible ref is Tom Anastasio's "Tutorial on Neural Systems Modeling" (Tom is actually a friend of mine since before I ever considered neuroscience).

If you're real interested and willing to put resources behind the interest, I've heard very good things about some of the Woods Hole courses, like http://hermes.mbl.edu/education/courses/special_topics/mcn.html

People study for years to get where your're trying to go.  The best recommendation you're likely to get is to hunt high and low for a collaborator to help you on your way.  Figure out what you bring to the table in such an arrangement, and find an engineer who might be interested in your field , likely a biomedical engineer.