Figure 4
A line graph showing the PDE residual distribution at t equals 0.5. The x axis represents the spatial coordinate ranging from 0.0 to 1.0. The y axis represents the physics residual ranging from negative 0.25 to 0.05. The graph includes two lines: a blue dashed line representing the fixed PINN model and an orange dashed line representing the GA-PINN model. The blue dashed line starts at approximately negative 0.05, peaks at around 0.05, dips to negative 0.25, and then rises again. The orange dashed line follows a similar pattern but with slightly different values. All values are approximated.Spatial distribution of the governing equation residual at for the fixed-weight and GA-optimized PINN models. The residual is evaluated along a representative spatial cross-section of the computational domain