Here's a fun suggestion. Go to
scholar.google.com and search for: "deep learning + <topic>". I did this for "weather prediction" and found a 2021 paper on the subject. From the conclusion:
"... there are specific properties of weather data which require the development of new approaches beyond the classical concepts from computer vision, speech recognition, and other typical ML tasks. Even though DL solutions for many of these issues are being developed, there is no DL method up to now which can deal with all of these issues concurrently as it would be required in a complete weather forecast system.
We expect that the field of ML in weather and climate science will grow rapidly in the coming years as more and more sophisticated ML architectures are becoming available and can easily be deployed on modern computer systems. ..."
So, there certainly are some areas where you'd expect deep learning to have surpassed the state of the art, where it hasn't (yet) done so. That said, the authors sound rather optimistic about its prospects.