MLPRegressor Output Range
Altough your data is between 0 and 1, the predictions can be outside of this range, as with any satistical model. This shows that you are not able to represent your data properly with your model. However, this is not the important point. If you want to ensure the outputs to be between 0 and 1, you have to change the relu activation for another one, such as sigmoid or softmax. These activations ensure that your outputs will be between 0 and 1, although they might lead to other problems, such as vanishing gradients. What is usually advised is to use relu layers until the last one, which has to be a sigmoid or a softmax.