  We construct the catalogues of standard sirens (StS) based on the future
gravitational wave (GW) detector networks, i.e., the second-generation
ground-based advanced LIGO+advanced Virgo+KAGRA+LIGO-India (HLVKI), the
third-generation ground-based Einstein Telescope+two Cosmic Explorer (ET+2CE),
and the space-based LISA+Taiji. From the corresponding electromagnetic (EM)
counterpart detectors for each networks, we sample from the probability of the
joint GW+EM detections to construct the Hubble diagram of standard sirens for
10 years detections of HLVKI, 5 years detections of ET+2CE, and 5 years of
detections of LISA+Taiji, which we estimate would be available and released in
the 2030s. Thus we construct a combined Hubble diagram from these ground and
spaced-based detector networks to explore the expansion history of our Universe
from redshift 0 to 7. We give a conservative and realistic estimation of the
catalogue and Hubble diagram of GW standard sirens and their potential on
studying cosmology and modified gravity theory in the 2030s. We adopt two
strategies for the forecasts. One is the traditional model-fitting Markov-Chain
Monte-Carlo method (MCMC). The results show that the combined StS alone can
constrain the Hubble constant at precision level $0.34\%$, 1.76 times more
tightly than the current most precise measurement from
\textit{Planck}+BAO+Pantheon. The joint StS with current EM experiments will
improve the constraints of cosmological parameters significantly. The modified
gravity theory can be constrained with $0.46\%$ error from the GW propagation.
In the second strategy, we use the machine-learning nonparametric
reconstruction techniques, i.e., the Gaussian process (GP) and also the
Artificial Neural Networks (ANN) as a comparison. GP reconstructions give
comparable results with MCMC. We anticipate more works and research on these
topics.
