The White Orphanage is an experimental facility disguised as an orphanage, and the place where Yulie and Kresnik Ahtreide were raised. The BGM that plays during this dungeon is In the Cold Iron Box (Disc 2, Track 1).
After the war ended, researchers continued their human experiments, and attempts at accelerated evolution on orphaned children. Most of their attempts to create Gene Drivers failed miserably, though they did have some success with Yulie. Though she couldn't activate dormant ARMs, she could control already active ARMs, most notably, the Guardian Programs.
By the time the party reaches the facility, it has long since been abandoned, though it does still contain much of the information the researchers managed to gather. This is also where the second battle with Jeremy Non takes place, and where the rest of the team meets Kresnik for the first time. Kresnik saves the party from being murdered by a vindictive Jeremy and inadvertently board the Eulalia.