Along with experiments, numerical simulations are key to gaining insight into the underlying mechanisms governing domain wall motion in thin ferromagnetic systems. However, a direct comparison between numerical simula- tion of model systems and experimental results still represents a great challenge. Here, we present a tuned Ginzburg–Landau model to quantitatively study the dynamics of domain walls in quasi two-dimensional ferromagnetic systems with perpendicular magnetic anisotropy. This model incorporates material and exper- imental parameters and the micromagnetic prescription for thermal fluctuations, allowing us to perform material-specific simulations and at the same time recover universal features. We show that our model quantitatively reproduces previ- ous experimental velocity-field data in the archetypal perpendicular magnetic anisotropy Pt/Co/Pt ultra-thin films in the three dynamical regimes of domain wall motion (creep, depinning and flow). In addition, we present a statistical analysis of the domain wall width parameter, showing that our model can pro- vide detailed nano-scale information while retaining the complex behavior of a statistical disordered model.