Figure 11.

The GP-smoothed PINN-evaluated $|h(x,t)|$ at different timeslices, $t=0,0.39,0.78,1.37$, from left to right. In this case the training data on the initial timeslice is subject to measurement errors, modeled by a Gaussian random variable with zero mean and a standard deviation of 0.1. GP-based smoothing was used on initial timeslice before training the PINN. The points marked with the blue cross (x) pointer in the leftmost set of plots indicate the samples on the initial timeslice used to fit the GP. The grey band in the subsequent plots represents the uncertainty associated with the PINN-evaluated approximation of $|h(x,t)|$.