Patema Inverted contains the anime movie directed by Yasuhiro Yoshiura.

Patema lives in an underground world of tunnels, the long-abandoned ruins of a giant industrial complex. Though she is a princess, she is held back by the rules imposed by the elders of her clan. One day when she is exploring in a forbidden zone, she is startled by a strange bat-like creature and tumbles headlong into a void – and out into the wide open world above the surface, a place with reversed physics, where if she let go she would “fall up” into the sky and be lost forever.

Age is a student on this surface world, a totalitarian society whose compliant population has been brainwashed against the “sinners who fell into the sky.” When he spies Patema hanging upside-down from a tree, he pulls her down to safety, struggling with all his might to keep her earthbound as she grips on to him for dear life. Together their weights cancel each other out, and once they master the art of navigating competing gravitational forces, they set out to evade the leaders of Age’s world and discover the secret that keeps their worlds apart.