So, what exactly is Ayato's character arc in The Asterisk War? There are three basic character arcs for the main character of a story: change, growth and flat.
The change arc is pretty obvious, it's the hero's journey. The protagonist has to overcome adversity, both internal and external. The external conflict represents a part of the internal conflict. At the end of the story, the hero is more aware of his own essence and enlightened about his place in the world. For example, Luke Skywalker changes over the course of Star Wars. The Luke we see at the beginning of A New Hope is not the same Luke we see at the end of Return of the Jedi.
The growth arc is similar to the change arc, but it's more focused on the hero's internal growth. The hero might not change much but he does gain a better understanding of himself and the world around him. For example, John Preston is basically the same character over the course of Equilibrium. He merely learns to accept emotions.
The flat arc is a bit more complicated because it involves change, but not for the protagonist. Instead, it's the change the protagonist brings to the world around him. In this arc, the character remains the same from beginning to end, but his actions and opinions change the world, presumably for the better. For example, Maximus from Gladiator doesn't really change; instead, he changes some people's mind about him, the emperor, the Roman Empire and gladiators in general.