  We investigate the out-of-equilibrium dynamics of a photo-excited
charge-density-wave (CDW) state in the square-lattice Holstein model, in a
setup similar to a pump-probe experiment. At half-filling, the ground state of
this system is characterized by a checkerboard modulation of particle
densities, accompanied by a concomitant lattice distortion. An efficient
real-space dynamics method integrating the von~Neumann equation for electron
density matrix and Newton equation for classical lattice dynamics is developed
to simulate the dynamical evolution of a photo-excited Holstein system. We find
that the energy injected by a short pump pulse results in the reduction of the
CDW order and the generation of coherent phonons. At strong photoexcitations,
while the CDW order is melted in the sense that the time-averaged order
parameter vanishes, a dynamical CDW state is self-sustained by the strong
coherent phonon oscillations. Our large-scale simulations further uncover a
dynamical regime of intermediate fluence where complex pattern formation is
induced by the pump pulse. The emergent spatial textures are characterized by
super density modulations on top of the short-range checkerboard CDW order. Our
demonstration of pattern formation highlights the significance of dynamical
inhomogeneity in quantum many-body systems in pump-probe experiments.
