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

Jun Li(李军),Yong Chen(陈勇)

Figure 2. One-soliton solution. Top: an exact one-soliton solution to the Burgers' equation is compared to the solution of the learned PDE (right panel). The system correctly captures the dynamics and accurately reproduces the solution with a relative ${{\mathbb{L}}}_{2}$ error of 2.45 × 10−03. Middle: comparison of the predicted solutions and exact solutions at the three temporal snapshots. Bottom: comparison between the corresponding predicted and exact solutions of the potential. The training process took approximately half a minute.