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

> Source: <https://arxiv.org/abs/2607.20541>
> Published: 2026-07-24 04:00:00+00:00

# Computer Science > Machine Learning

[Submitted on 10 Jul 2026]

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

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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.

## Submission history

From: Hossein Nick Zinat Matin [[view email](/show-email/b7e10e1c/2607.20541)]

**[v1]** Fri, 10 Jul 2026 21:20:17 UTC (21,504 KB)

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