Helle, this is my second kid with them. Nate's are so much worse than Darc's were. They sound exactly what we go through every night.
No there really isn't anything you can do. It's their brain going from one sleep cycle to the next with a few hiccups. Generally they are at the same time, but not always and some kids have triggers. Others don't.
As hard as it is, touching and speaking stimulate their brain and waking/stimulating makes them worse.

When they're staring right through you screaming and screaming and don't even know you're there...that's what I find really hard.
I was nearly going to post last night about them.

babe. Hope they're only in your house for a short stay.