Brynhildr in the Darkness Gokukoku no Brynhildr

The original manga revolves around high school boy Ryōta Murakami, who cannot forget his female childhood friend whom he let die in an accident. Feeling that he must fulfill their promise of proving the existence of aliens, he has continuously looked up at the sky as a member of the astronomy club. One day, a girl named Neko Kuroha who looks exactly like his childhood friend appears as a transfer student. It turns out that she is a magic-user that has run away from a research lab.

(Source: Anime News Network)