Figure 20.

The leftmost column shows the exact solution for 2D Burgers’ equation at $t=0.1579$ (first and third row from top for $(x,y,t)$) and $t=0.6316$ (second and fourth row from top for $v(x,y,t)$). The remaining columns show the point-wise error in PINN-evaluated solution for noise-free PINN (second column), noisy PINN without smoothing (third column), GP-PINN (fourth column), and SGP-PINN (final i.e. fifth column). Except the vanilla PINN (no error), all models were trained with data sampled from the initial timeslice corrupted with additive Gaussian noise with zero mean and $\sigma =0.5$.