How to constraint the Gaussian process model output ranging between 0 and 1? It requires the Gaussian process model output ranging between 0 and 1, is there any technique to constrain the Gaussian process model's output?

If you make an assumption that $y$ follows a bounded distribution, it should eb possible to devise an appropriate Gaussian Process that respects that assumption.
If, for example, $y$ is Beta-distributed, see:

*

*Jensen, Bjørn Sand, Jens Brehm Nielsen, and Jan Larsen. "Bounded gaussian process regression." 2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP). IEEE, 2013.
