  The success of the multi-messenger astronomy relies on gravitational-wave
observatories like LIGO and Virgo to provide prompt warning of merger events
involving neutron stars (including both binary neutron stars and
neutron-star-black-holes), which further depends critically on the
low-frequency sensitivity of LIGO as a typical binary neutron star stays in
this band for minutes. However, the current sub-60 Hz sensitivity of LIGO has
not yet reached its design target and the excess noise can be more than an
order of magnitude below 20 Hz. It is limited by nonlinearly coupled noises
from auxiliary control loops which are also nonstationary, posing challenges to
realistic early-warning pipelines. Nevertheless, machine-learning-based neural
networks provide ways to simultaneously improve the low-frequency sensitivity
and mitigate its nonstationarity, and detect the real-time gravitational-wave
signal with a very short computational time. We propose to achieve this by
inputting both the main gravitational-wave readout and key auxiliary witnesses
to a compound neural network. Using simulated data with characteristic
representing the real LIGO detectors, our machine-learning-based neural
networks can reduce nonlinearly coupled noise by about a factor of 5 and allows
a typical binary neutron star (neutron-star-black-hole) to be detected 100 s
(10 s) before the merger at a distance of 40 Mpc (160 Mpc). If one can further
reduce the noise to the fundamental limit, our neural networks can achieve
detection out to a distance of 80 Mpc and 240 Mpc for binary neutron stars and
neutron-star-black-holes, respectively. It thus demonstrates that utilizing
machine-learning-based neural networks is a promising direction for the timely
detection of the coalescence of electromagnetically bright LIGO/Virgo sources.
