Hayao Miyazaki, who criticized the film for "trying to make a Zero fighter story based on a fictional war account that is a pack of lies" had months before released The Wind Rises (2013), a film about the designer of the same aircraft depicted in this film.
It's easy to believe that Miyabe's carrier is the Kaga, since it's the first to get hit. But in fact his carrier is the flagship Akagi, which you can tell from the "A" painted on the deck.
The US carrier under attack by Miyabe at initial and final moments of the movie is the USS Ticonderoga (CV-14, as seen painted on deck) which was in fact hit by a kamikaze on 21 January 1945 wile performing operations near Formosa (Taiwan). The ship was hit by another kamikaze immediately afterwards but as she appeared undamaged at the moment of Miyabe plunge attack, he is pictured as the first one at the movie. Good to know the production payed attention at these details.
The author of the book this film is based on, Naoki Hyakuta, is controversial for his nationalistic far right views and denial of Japanese war crimes.