  We study global-in-time dynamics of the stochastic nonlinear beam equations
(SNLB) with an additive space-time white noise, posed on the four-dimensional
torus. The roughness of the noise leads us to introducing a time-dependent
renormalization, after which we show that SNLB is pathwise locally well-posed
in all subcritical and most of the critical regimes. For the (renormalized)
defocusing cubic SNLB, we establish pathwise global well-posedness below the
energy space, by adapting a hybrid argument of Gubinelli- Koch-Oh-Tolomeo
(2022) that combines the $I$-method with a Gronwall-type argument. Lastly, we
show almost sure global well-posedness and invariance of the Gibbs measure for
the stochastic damped nonlinear beam equations in the defocusing case.
