In such systems, even if we have a perfect model we cannot know the initial conditions with sufficient accuracy to make reliable long term predictions. This is not just a limit of our current technology, but a property of chaotic systems. If weather is a chaotic system, then we will never make serious progress beyond short term forecasts.
If you don't know what the initial conditions are, how will AI help?
http://www.freakonomics.com/2011/09/27/an-algorithm-that-can...
“Only about 15% of what we do is traditional forecast meteorology,” says CEO Bill Kirk
I once had a brief conversation with a meteorology student about this. The idea of learning a model from example data seemed foreign to him. It seemed to me that there could be things to improve by applying ML algorithms.
Basically they do it and then use their models to sell more accurately priced insurance.