  The gravitational waves from compact binary systems are viewed as a standard
siren to probe the evolution of the universe. This paper summarizes the
potential and ability to use the gravitational waves to constrain the
cosmological parameters and the dark sector interaction in the Gaussian process
methodology. After briefly introducing the method to reconstruct the dark
sector interaction by the Gaussian process, the concept of standard sirens and
the analysis of reconstructing the dark sector interaction with LISA are
outlined. Furthermore, we estimate the constraint ability of the gravitational
waves on cosmological parameters with ET. The numerical methods we use are
Gaussian process and the Markov-Chain Monte-Carlo. Finally, we also forecast
the improvements of the abilities to constrain the cosmological parameters with
ET and LISA combined with the \it Planck.
