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Weather forecasting is difficult problem but it's problem that as far as I know has been worked on intensely for quite a while.

Weather forecasting is based on physics-based models that, so far as I know, are essentially correct with the fundamental barrier to prediction being a combination of random effects and the difficulty of solving the complex equations numerically.

Deep learning involves training a heuristically approximate a system based on past data. It has been used to emulate various human-learning behaviors like recognizing images or recognizing good or bad position in games. Essentially, the visible successes are in "we don't know but can extrapolate roughly from data" (or we "know" but can't easily program it, in the case of image recognition). So I'd be surprised if deep learning do a good or better job in situation where we do know how things work, we already running algorithm which is correct - the situation with weather.




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