Errr... no. If your child invents something, it does NOT make it your invention. The "art" in here was created on its own digitally, with numbers behind it, and not because of its own imagination. It was created by a machine. It's just algorithm.
In fact it does make it yours as long as the child is under your protection. You basically are responsible for everything the child does, right or wrong. If it steals your neighbor's car and crashes it who is going to pay? You. If the child crawls under your car and you happen to drive over it not knowing it was there you will get charged. If the child happens to earn money for an invention you will get that money, as the caretaker/parent takes care of the finances, legal proceedings and such.