  Impact of noise in coupled oscillators with pairwise interactions has been
extensively explored. Here, we study stochastic second-order coupled Kuramoto
oscillators with higher-order interactions, and show that as noise strength
increases the critical points associated with synchronization transitions shift
toward higher coupling values. By employing the perturbation analysis, we
obtain an expression for the forward critical point as a function of inertia
and noise strength. Further, for overdamped systems we show that as noise
strength increases, the first-order transition switches to second-order even
for higher-order couplings. We include a discussion on nature of critical
points obtained through Ott-Antonsen ansatz.
