  We perform a numerical study on the two-dimensional nonequilibrium
exciton-polariton systems driven by incoherent pumping based on the stochastic
generalized Gross-Pitaevskii equation. We calculate the density fluctuation,
coherence function, and scaling function. It is found that the correlations at
short range agree with the Bogoliubov linear theory. While at large distance,
both static and dynamic correlations are characterized by the nonlinear scaling
behaviors of Kardar-Parisi-Zhang (KPZ) universality class, especially when the
interaction is weak. In this regime, scaling analyses are crucial to capture
the universal KPZ scaling features. In addition, the interaction between
vortices is modified in the strong KPZ regime and leads to complex
nonequilibrium vortex patterns.
