In the 3 in-game difficulties, you are able to check your progress at the plaque in Act 3, Sarn Encampment. Without doing a map run, is it possible to check your current completed trials?
As of 3.0 there is a way to check the progress outside of maps.
Once in the Aspirants' plaza, the new "Labyrinth activation device" will show your current progress:
As I show in the image, by going with the mouse over one of the icons will show you which trial it refers to.