Not that I've heard of I would think that for a blockbuster franchise film, there would be some word about official start date, but that's just a guess. (He was supposed to have filmed something in June, but that one has been under the radar, if even true, but they probably can't get away with it for a bigger film like this).
IMdB is pretty reliable about film timelines. Until a film gets its funding together it will just be announced. Then it moves to pre-production when actors and crew are being hired. Next, filming and then post-production.
I remember watching the original on black and white TV eons ago -- what jewels we got to watch for free in those years. The Invisible Man was wrapped in bandages, and periodically, he removed the bandages and you'd see something moved, etc. I liked the old horror stuff -- sitting here I can literally "hear" Claude Rains voice, which is a long, long time to hold onto a memory. Old horror movies aren't so much terrifying as they are suspenseful. And the sets are fairly simple, add in the black and white, and there's not alot to distract one from the acting. So I am hoping that this update will totally capture that original vibe.
In other news, though sorry, I didn't post about it and don't remember where I read it, someone (is it Marvel?) is suing over the "Dark Universe" title, so don't be too surprised if they have to change the name of the franchise (Dark World? )