How Scientists Taught AI to Handle Shock Waves

This article demonstrates a proof-of-concept for training neural networks with JAX to solve PDEs, focusing on shock wave problems. The authors propose NDNN (Novel Deep Neural Networks) as a more accurate alternative to PINNs, running experiments with tanh networks and validating convergence through 1- and 2-shock wave tests. Results show NDNN produces stable, reliable approximations where PINNs fail, highlighting JAX’s ease of implementation and robustness in practical low-dimensional setups.