Solving second-order nonlinear evolution partial differential equations using deep learning*

Jun Li(李军),Yong Chen(陈勇)

Figure 8. Exponential initial condition. Top: a solution to the Burgers' equation is compared to the corresponding solution to the learned PDE. The model approximately captures the nonlinear dynamics and reproduces the solution with a relative ${{\mathbb{L}}}_{2}$ error of 1.05 × 10−01. Bottom: comparison between the predicted solution and exact solution at the snapshots. The model training took approximately 12 min.