A Radical Neural Network Approach to Modeling Shock Dynamics

This paper introduces a non-diffusive neural network (NDNN) method for solving hyperbolic conservation laws, designed to overcome the shortcomings of standard Physics-Informed Neural Networks (PINNs) in modeling shock waves. The NDNN framework decomposes the solution domain into smooth subdomains separated by discontinuity lines, identified via Rankine-Hugoniot conditions. This approach enables accurate tracking of entropic shocks, shock generation, and wave interactions, while reducing the diffusive errors typical in PINNs. Numerical experiments validate the algorithm’s potential, highlighting its promise for extending shock-wave computations to higher-dimensional problems.