Could you explain the link you're making here? As far as I understand four colour theorem was computer assisted proof in the sense that mathematicians wrote a very specific and analytical definition for it in a logical theorem prover.
The linked article is very different right? Because it's using a neural net to do some kind of probabilistic inference as a heuristic for imperfectly stimulating physical events.
Exactly; it's about generating (much faster) heuristics for "guessing" the outcome given certain parameters, instead of running the real simulation every time. Useful, for sure, but the real thing should be used to verify once you've found something interesting.
My bad, I though it was a deterministic system, not probabilistic.