摘要：我们提出 HypNO，这是一种面向标量双曲守恒律的图神经算子。HypNO 直接在由有限体积单元构成的时空图上运行，并采用按邻接关系分解、融入物理信息的消息传递机制，以遵循激波附近的迎风格式和熵可容许性。我们在 Lighthill-Whitham-Richards（LWR）和 Aw-Rascle-Zhang（ARZ）交通流模型上对该架构进行了基准测试；由于这些模型同时具有全局输运和激波形成特征，它们是对算子学习方法的压力测试。HypNO 能够在一系列初始条件下准确预测解的快照，同时捕捉解中的激波与不连续性。

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.