Arpeggio of Blue Steel -Ars Nova-

Arpeggio of Blue Steel -Ars Nova- is a 2013 anime adaptation of Arpeggio of Blue Steel (plus a Compilation Movie, -Ars Nova DC-, and a sequel, -Ars Nova Cadenza-, in 2015). In 2039, humanity is cut off from the sea by the Fleet of Fog, a fleet of incredibly advanced robotic warships that intercept and destroy any vessel that intrudes into the water (or the air or space above it). Without sea commerce, humanity is doomed to a slow, lingering extinction, but in 2056, there is hope with the invention of the vibration warhead torpedo, a weapon that can annihilate a Fog warship in one strike. However, Japan lacks the resources to mass-produce them, so they contract the Blue Steel, a group of mercenaries with a Fog defector (the submarine I-401, known to the crew as "Iona"), to carry the warhead prototype across the ocean to America, where they will be mass-produced to turn the tide.

Tropes used in Arpeggio of Blue Steel -Ars Nova- include:

Arc Words: Where do we come from? What are we? Where are we going?
Art Shift: The Concept Comm System is an austere, 2D-animated world, whereas the real world is (usually, though not 100% consistently) based on 3D animation converted to cel-shading. The CCS also shifts over time, growing from an austere gazebo in a white void to a natural setting as more of the Fog ships using it develop human emotions. It then becomes a Room Full of Crazy after Kongou's Villainous Breakdown. Also, when a superbattleship hosts the CCS, it is a much larger space than when a 'mere' fast battleship or heavy cruiser is hosting.
Conspicuous CG: Intentionally used to emphasize the inhuman nature of the Fog ships.
Humanity Ensues: The unintentional side-effect of creating Mental Models and interacting with humanity.
Humanity Is Infectious: Every single Fog ship that Gunzou and Iona come into contact with is changed from the encounter. Not always for the better. When Kongou meets Gunzou for parley, she leaves her core behind on her ship body (rather than bringing it in her Mental Model as the others do) in the hopes of avoiding it. It doesn't work.
Humanity Is Insane: Kongou forms this opinion as she sees each of her fleet-mates come into contact with Gunzou and Iona and develop "errors".
Humans Are Special: The Fleet of Fog created Mental Models for themselves in an attempt to grow and develop the adaptability they observed in humans during the course of their blockade. For some of them, it worked a little too well. (Funnily enough, most of the human characters in -Ars Nova- are pretty flat and static -- there's less than 6 hours of total screen time in the anime and sequel movie, and most of the non-battle time is spent on the Mental Models and their interactions and growth.)
Robot Names: Iona comes from the designation I-401 (I-yon...).
Shipper on Deck: Hyuga ships (heh!) Takao with Gunzou (not so much for Takao's sake, but to get Gunzou away from Iona so that she can have her).
Shout-Out:
- Kyouhei comments "That's no battleship!" when he sees Kongou's monstrous airship form -- which itself superficially resembles the Death Star.
- Some of the show's visual style appears to inherit from Neon Genesis Evangelion:
  - The flashing text in the opening (much as NGE had "Absolute Terror Field", "Third Impact", and the like, Ars Nova has "Human Extinction", "Mental Model", "Vibration Warhead", etc.)
  - The battle theme heard in e.g. the battle against Haruna and Kirishima sounds like The Beast II.
  - The Conspicuous CG used on the Fog battleships and their Klein field manipulations visually resembles the Angels and their AT Fields, especially as seen in Rebuild of Evangelion.
Spaceship Girl: Called "Mental Models", the Fog ships formed them to attempt to learn from humanity and improve themselves. They got quite a bit more than they bargained for.
Villainous Breakdown: For all her devotion to the Admiralty Code and her attempts to avoid being infected by humanity, Kongou suffers a pretty severe one in the final third of the series, at first attempting to deny that she has an obsession with Iona (in spite of the evidence to the contrary), and then taking a flying leap off the edge when she is relieved of command by I-400 and I-402, eventually breaking free of her lockdown by sheer willpower -- when she would have scoffed at the notion earlier in the series -- and destroying the American Fleet of Fog so that she can destroy Iona herself and destroy herself in the process, as she has "succumbed" to the same "error" she saw in the rest of her fleet.