Figure 19.

The initial condition $u(x,y,t=0)$ for 2D Burgers’ equation for (a) error-free PINN, (b) noisy PINN without smoothing, (c) noisy PINN with GP smoothing, (d) noisy PINN with SGP smoothing. The figures in the second row show the error in PINN-evaluated solution at the initial timeslice for the corresponding architecture in the top row. The final two rows show the equivalent distributions for the $v(x,y,t)$ field. 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 σ = 0.5.