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How about a neural network model predicting where the player will be in one second, and center the camera there?

That lets the player see where they're going.

The network would have the local game map (including enemys positions and velocities), together with a few seconds of player history as input. It could be trained on beta users.

This is like training a neural net to solve algebra problems instead of just solving the algebra problems.
Well at least the training data won't be hard to generate?
How do you predict when the player will be in one second? I feel like this will make for jerky camera movements when the player makes sudden moves. In the end you will have to do some smooth movements like mentioned in this article.
You might have missed the conclusion:

  All this results in a dynamic camera behaviour that works
  95% of the time, while giving you the tools to manually 
  design the camera’s behaviour in those remaining
  situations for gameplay reason or dramatic effect.
No neural net black box will give you this amount of accuracy. Not to mention the ability to manually design exceptions.
This is using the wrong tool to solve the problem. Could it work? Sure. Is it a good solution? No.
The camera in Super Mario World worked at very similarly in 1991. Isn't this stuff pretty standard by now?