Can Neural Networks Capture Shock Waves Without Diffusion? This Paper Says Yes

This paper explores the limits of standard Physics-Informed Neural Networks (PINNs) in handling shock waves in hyperbolic conservation laws, where artificial diffusion is typically added to approximate solutions. Instead, the authors introduce a non-diffusive neural network (NDNN) method that directly computes entropic shock waves without artificial viscosity. The approach is derived, implemented, and validated through multiple experiments—including shock wave interaction and generation—demonstrating convergence, accuracy, and efficiency for complex PDE systems.