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

Jun Li(李军),Yong Chen(陈勇)

Figure 1. Cosine initial condition. Top: an exact solution to the Burgers' equation is compared to the corresponding solution of the learned PDE. The model correctly captures the dynamics behavior and accurately reproduces the solution with a relative ${{\mathbb{L}}}_{2}$ error of 9.21 × 10−03. Bottom: comparison between the predicted solutions and exact solutions at the three snapshots (corresponding to the vertical lines in the top panel). The model training took about 19 min.