  The search for multi-messenger signals of binary black hole (BBH) mergers is
crucial to understanding the merger process of BBH and the relative
astrophysical environment. Considering BBH mergers occurring in the active
galactic nuclei (AGN) accretion disks, we focus on the accompanying high-energy
neutrino production from the interaction between the jet launched by the
post-merger remnant BH and disk materials. Particles can be accelerated by the
shocks generated from the jet-disk interaction and subsequently interact with
the disk gas and radiations to produce high-energy neutrinos through hadronic
processes. We demonstrate that the identification of the high-energy neutrino
signal from BBH merger in AGN disks is feasible. In addition, the joint BBH
gravitational wave (GW) and neutrino detection rate is derived, which can be
used to constrain the BBH merger rate and the accretion rate of the remnant BH
based on the future associated detections of GWs and neutrinos. To date, an
upper limit of BBH merger rate density in AGN disks of $R_0 \lesssim 3\,\rm
Gpc^{-3} yr^{-1}$ is derived for the fiducial parameter values based on the
current null association of GWs and neutrinos.
