Isn't Physics trying to describe the natural world? I'm guessing you are taking two positions here that are causing me confusion with your statement: 1) that our minds can be explained strictly through physical processes, and 2) our minds, including our intelligence, are outside of the domain of Physics.
If you take 1) to be true, then it follows that Physics, at least theoretically, should be able to explain intelligence. It may be intractably hard, like it might be intractably hard to have physics decribe and predict the motions of more than two planetary bodies.
I guess I'm saying that Physical laws ARE natural laws. I think you might be thinking that natural laws refer solely to all that messy, living stuff.