Figure 5.

Example 3.2: inviscid Burgers' equation with noise =73.7%. The space–time dynamics are plotted to provide a qualitative comparison between the original simulation (a) and the learned dynamics (b) over time. The error between the original simulation and the learned solution is small in norm: the L¹ error is 0.0163, the L² error is 0.0193 and the $L^{\mathrm{\infty }}$ error is 0.2705, which also includes the projection errors (difference in grid sizes). The horizontal axis is space and the vertical axis is time. (Online version in colour.)