  Although the spatial curvature has been precisely determined via the cosmic
microwave background (CMB) observation by Planck satellite, it still suffers
from the well-known cosmic curvature tension. As a standard siren,
gravitational waves (GWs) from binary neutron star mergers provide a direct way
to measure the luminosity distance. In addition, the accelerating expansion of
the universe may cause an additional phase shift in the gravitational waveform,
which allows us to measure the acceleration parameter. This measurement
provides an important opportunity to determine the curvature parameter
$\Omega_k$ in the GW domain based on the combination of two different
observables for the same objects at high redshifts. In this study, we
investigate how such an idea could be implemented with future generation of
space-based DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO)
in the framework of two model-independent methods. Our results show that DECIGO
could provide a reliable and stringent constraint on the cosmic curvature at a
precision of $\Delta\Omega_k$=0.12, which is comparable to existing results
based on different electromagnetic data. Our constraints are more stringent
than the traditional electromagnetic method from the Pantheon SNe Ia sample,
which shows no evidence for the deviation from the flat universe at $z\sim
2.3$. More importantly, with our model-independent method, such a
second-generation space-based GW detector would also be able to explore the
possible evolution $\Omega_k$ with redshifts, through direct measurements of
cosmic curvature at different redshifts ($z\sim 5$). Such a model-independent
$\Omega_k$ reconstruction to the distance past can become a milestone in
gravitational-wave cosmology.
