Neural Networks vs. Scalar Shock Waves

This article introduces a non-diffusive neural network (NDNN) solver for one-dimensional scalar hyperbolic conservation laws (HCLs) containing shock waves. The approach models both smooth solutions and discontinuity lines using neural networks, first for a single shock wave and then for multiple shocks. It also addresses shock generation, shock–shock interaction, and extensions to systems, showing how 2D+1 neural networks can be applied to approximate solutions in complex PDE scenarios.