HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws

Abstract:We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws. HypNO operates directly on a space-time graph of finite-volume cells and uses adjacency-factored, physics-informed message passing to respect upwinding and entropy admissibility near shocks. We benchmark the architecture on the Lighthill-Whitham-Richards (LWR) and Aw-Rascle-Zhang (ARZ) traffic-flow models, a stress test for operator-learning methods because of their simultaneous global transport and shock formation. HypNO predicts solution snapshots accurately across a range of initial conditions while capturing the shocks and discontinuities of the solution.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2607.20541 [cs.LG]

(or arXiv:2607.20541v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.20541 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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