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

Jun Li(李军),Yong Chen(陈勇)

Figure 4. Two-soliton solution. Top: an exact two-soliton solution to the Burgers' equation (left panel) is compared to the corresponding reconstructed solution of the learned PDE. The system correctly captures the nonlinear dynamics and reproduces the solution with a relative ${{\mathbb{L}}}_{2}$ error of 4.23 × 10−03. Middle: comparison between the predicted and exact dynamics at the temporal snapshots. Bottom: comparison between the potential behaviors. The training took approximately 6.5 min.