The framing for arched ceilings is usually engineered and pre-manufactured, then delivered and installed as a kit. You'd really want a specialized engineering firm making the kit because there are many ways to mess it up. You can arch drywall, provided the curvature is not too small of course. 1/4" flexes enough by itself and you can spray the back of 1/2" with water and that will make it pliable just enough.Â
I wanted to include some videos here, see below. it's just one of the specialized firms, not an enforcement. But they do make videos and provide other info that explains the process pretty well.
Should we assume it's your dream home and no expense is spared, right? Just checking ... I would take their claims of ease of self-install with a grain of salt. You do want a crew that has had to deal with arched ceilings before, especially if you're getting into wetting drywall etc. Good luck!
Barrel vault ceiling video:
Drywall on arched ceilings video: