Xuan-Jie Wang

An adaptive weighted extrapolation neural network for dispersive shock waves generated by square-root initial condition of the KdV equation

Simulating dispersive shock waves (DSWs) using physics-informed neural networks (PINNs) presents significant numerical difficulties. In particular, the square-root initial condition exhibits singularity near the origin, making it difficult to fit accurately. This initial fitting error is amplified through nonlinear evo...