In the beginning, their relationship would likely be a bit rocky. Artemis is a goddess of the hunt and virginity, so having a husband is a big change. Percy would have to be patient and understanding. Over time, they would bond over their mutual respect for nature. Percy might teach Artemis about the modern human world, and she could teach him about the ancient ways of the gods. Their relationship would develop as they face challenges together, like threats to the natural order of things. They would become more in sync, with Percy supporting Artemis in her divine duties and Artemis protecting Percy in the dangerous world of the gods.
Their relationship would start with a sense of mystery. Percy is not a typical partner for Artemis. As time progresses, they would have to deal with the reactions of the other gods and goddesses. Some might be jealous, some might be disapproving. But through it all, Percy and Artemis would find strength in each other. Percy's courage and determination would attract Artemis, and her grace and power would amaze Percy. They would go through different phases in their relationship. Maybe at first it's just a mutual admiration, then it turns into a deep love as they get to know each other better. Their relationship would also be shaped by the events around them, like wars among the gods or the appearance of new threats to the cosmos.