A Structure-Preserving Graph Neural Solver for Parametric Hyperbolic Conservation Laws

ArXi:2604.15617v1 Announce Type: cross Hyperbolic conservation laws govern a wide range of transport-driven dynamics featuring shocks, contact discontinuities, and complex wave interactions, posing distinct challenges for deep-learning-based surrogate modeling. While classical numerical methods provide robust and physically admissible solutions, their computational cost restricts applicability in many-query tasks such as parametric studies and design optimization.