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

Jun Li(李军),Yong Chen(陈勇)

Figure 12. Another hyperbolic secant initial condition. Top: a solution to the Burgers' equation is compared to the solution of the learned PDE. The system correctly captures the dynamics and reproduces the solution with a relative ${{\mathbb{L}}}_{2}$ error of 4.59 × 10−02. Bottom: comparison between the predicted solution and the exact solution at the snapshots. The training process took approximately 42 min.