Figure 5.

(a) Graphical representation of the angles ω_data (the smaller angle in (a)) and ω_model (the larger angle in (a)), identified respectively by the variation Δ(t_y+1) at time t_y and the predicted variation of the model at the same time $-\mathrm{\nabla }H(\mathbf{x}(t_y))$, and by the two subsequent variations Δ(t_y) and Δ(t_y+1). (b) Comparison between the angle ω_data between the velocity of the system at consecutive times and the angle ω_model between the velocity of the system and the velocity predicted by equation (2.5). (c) Variations Δx_i(t_y) for all the components i of the feature vector in the same two cases. In the inset, we show the same comparison excluding communes with a population larger than 10⁴.