It's not magic, so is it safe to assume the ANN is quickly narrowing down the search space by eliminating the possibilities that were not showing up as patterns

It's not magic, so is it safe to assume the ANN is quickly narrowing down the search space by eliminating the possibilities that were not showing up as patterns in training set therefore limiting the search to a finite subset of infinite set of possible behaviors of the system? If the chaos produces a new kind of behavior the result of the ANN may be totally wrong. In other words - it works well, often. Is my simplistic thinking right?