Figure 16.

The initial condition at t = 0 for 2D heat equation for (a) error-free PINN, (b) noisy PINN without smoothing, (c) noisy PINN with GP smoothing, (d) noisy PINN with SGP smoothing. 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 = 1.0. The figures in the bottom row show the error in PINN-evaluated solution at the initial timeslice for the corresponding architecture in the top row.