This is essentially the same exact problem as a classic chess playing program, recursively computing all possibilities N moves ahead, and an AI which "groks" the game's patterns and knows where to focus fewer resources with greater success.
This translates especially well to games like Go, where computing all moves is not even pragmatically possible the classic way. But AI beats the best Go players.
Raw models are excellent for establishing the theory, and for training the AI. But... the AI is better at figuring out more effective, precise, and efficient model within itself, based on both synthetic (based on models) and real data (actual weather patterns).
EDIT: And just to point out, this is not just an AI phenomenon. You are a neural network. And "intuition" is the sense of predicting outcomes you develop, without knowing how and why precisely. This is why I frown upon people with academic knowledge who dismiss people with say engineering or other practical experience in a field. A farmer may not tell you why doing things a weird way results in amazing crop yields, but he gets the gains, and when theory doesn't correlate with reality, it's not reality that's wrong, but the theory.
To recap, nothing beats "learning by example". And AI learns by example. Of course, the formal theoretic models that we can collectively share, explain, and evolve over time have their own strong benefits and have allowed us to grow as a civilization. Computers are in effect "formal computation machines". I don't think we'll run AI for long on digital circuits and it's a clumsy workaround. Computers will have analog processing units for AI and digital processing units for cold, hard logic and data. And the combination is the most powerful approach of all.