RahXephon: Pluralitas Concentio(2003)

Ayato and Haruka are middle-school sweethearts whose lives take a dire turn when the mysterious Mu invade Tokyo in the year 2012. Protecting humanity from the Mu may be Ayato's destiny, but what he really wants is to regain the relationship he once had with Haruka... a love that will have to transcend space, time, and reality itself.