Crystal Cage

Alyssa's father wants her to settle down and become a happy wife and mother, as befitting a woman from one of the noble Houses, but Alyssa has other ideas: she wants to be an inventor. Her first invention, the crystal-powered teacup warmer, has earned her an invitation to study at the Institute and she accepts, hoping to meet her personal heroine Lady Isabelle and to be herself outside the confines of her rigid upbringing.
Left disappointed when Lady Isabelle proves to be dismissive, Alyssa is soon captivated anew by Prince Artan, who hides a secret himself and teaches Alyssa far more than the technology she's come to study. But relationships between teachers and students are forbidden by the Institute, and they aren't the only ones who will suffer should they get caught.