  High-velocity neutron stars (HVNSs) that were kicked out from their birth
location can be potentially identified with their large proper motions, and
possibly with large parallax, when they come across the solar neighborhood. In
this paper, we study the feasibility of hunting isolated HVNSs in wide-area
optical surveys by modeling the evolution of NS luminosity taking into account
spin-down and thermal radiation. Assuming the upcoming 10-year VRO LSST
observation, our model calculations predict that about 10 HVNSs mainly
consisting of pulsars with ages of $10^4$--$10^5$ yr and thermally emitting NSs
with $10^5$--$10^6$ yr are detectable. We find that a few NSs with effective
temperature $< 5 \times 10^5$ K, which are likely missed in the current and
future X-ray surveys, are also detectable. In addition to the standard neutron
star cooling models, we consider a dark matter heating model. If such a strong
heating exists we find that the detectable HVNSs would be significantly cooler,
i.e., $\lesssim 5\times 10^5$ K. Thus, the future optical observation will give
an unique NS sample, which can provide essential constraints on the NS cooling
and heating mechanisms. Moreover, we suggest that providing HVNS samples with
optical surveys is helpful for understanding the intrinsic kick-velocity
distribution of NSs.
