Back in 2013 I was one of the first to try to answer the question of whether works generated by AIs were covered by copyright law. The answer back then was "it depends", and absent definitive court rulings we're still waiting to see how this issue will play out.
In the years since we've seen the monkey selfie story reinforce the idea that only a person can author a work, so one might think this matter settled. However, that case involved an animal, and there is existing case law and copyright law that covers databases, so this is very much up in the air.
Last month the 1709 blog analyzed this issue from the perspective of EU law, and expressed doubt that an AI work can be copyrighted.