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

Jun Li(李军),Yong Chen(陈勇)

Figure 6. Another two-soliton solution. Top: an exact two-soliton solution to the Burgers' equation (left panel) is compared to the solution of the learned PDE. The system correctly captures the nonlinear dynamics and accurately reproduces the solution with a relative ${{\mathbb{L}}}_{2}$ error of 3.50 × 10−03. Middle: comparison between the predicted and exact solutions at the three temporal snapshots. Bottom: comparison between the corresponding predicted and exact solutions of the potential. The model training took about 3.5 min.