Understanding the spontaneous emergence of patterns on laser-irradiated surface has been a topic of interest for many years. Brought far from equilibrium under ultrafast photoexcitation, the material exhibits topographic surfaces that reveal signatures from multiphysical coupling, interrogating on the principal mechanism that drives the organisation nature. Some laser-induced periodic surface structures reveal periods typic from electromagnetics, nonlinear optics and plasmonic origin whilst others are characteristic of fluid dynamics or even thermochemical reactions. However, upon multi-shot irradiation, liquid flows are driven by laser-induced energy gradients and patterns are unstable leading to a variety of possible states, including hybrid states of bistable patterns and chaos. Stable spatially-periodic patterns typically arise through small, localized perturbations of the underlying optical coupling on random nanoreliefs. These perturbations grow in amplitude until nonlinear saturation takes over while, at the same time, the nascent topography disturbs the optical response. Whereas the spatially uniform growth into a pattern that can be described within the classic Maxwell and Navier-Stokes equations, the propagation, spatial competition of modes and bifurcation regime require nonlinear dynamics that mimic the behavior of the excited systems near the onset of convective instabilities. One of the challenges is to develop a general and efficient model that inherit relevant symmetry and scale invariance properties and that contain the stochasticity (emergence) and nonlinear properties (dynamics) able to reproduce dissipative structures in spatially extended systems. A stochastic Swift-Hohenberg modelling is then proposed to reproduce hydrodynamic fluctuations at the convective instability threshold that has been recently demonstrated as the very nature of the laser-induced self-organized nanopatterns.