{"slug": "hypno-a-graph-based-neural-operator-with-physics-informed-message-passing-for", "title": "HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws", "summary": "Researchers introduced HypNO, a graph-based neural operator for scalar hyperbolic conservation laws that uses physics-informed message passing to respect upwinding and entropy admissibility near shocks. The architecture, benchmarked on the Lighthill-Whitham-Richards and Aw-Rascle-Zhang traffic-flow models, accurately predicts solution snapshots across a range of initial conditions while capturing shocks and discontinuities.", "body_md": "# Computer Science > Machine Learning\n\n[Submitted on 10 Jul 2026]\n\n# Title:HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws\n\n[View PDF](/pdf/2607.20541)\n\n[HTML (experimental)](https://arxiv.org/html/2607.20541v1)\n\nAbstract: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.\n\n## Submission history\n\nFrom: Hossein Nick Zinat Matin [[view email](/show-email/b7e10e1c/2607.20541)]\n\n**[v1]** Fri, 10 Jul 2026 21:20:17 UTC (21,504 KB)\n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer\n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers\n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps\n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations\n\n*(*[What are Smart Citations?](https://www.scite.ai/))# Code, Data and Media Associated with this Article\n\nalphaXiv\n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers\n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub\n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub\n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face\n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast\n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower\n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender\n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))\nIArxiv Recommender\n\n*(*[What is IArxiv?](https://iarxiv.org/about))# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.\n\nHave an idea for a project that will add value for arXiv's community? [ Learn more about arXivLabs](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/hypno-a-graph-based-neural-operator-with-physics-informed-message-passing-for", "canonical_source": "https://arxiv.org/abs/2607.20541", "published_at": "2026-07-24 04:00:00+00:00", "updated_at": "2026-07-24 04:12:58.547139+00:00", "lang": "en", "topics": ["machine-learning", "neural-networks", "ai-research"], "entities": ["HypNO", "Lighthill-Whitham-Richards", "Aw-Rascle-Zhang"], "alternates": {"html": "https://wpnews.pro/news/hypno-a-graph-based-neural-operator-with-physics-informed-message-passing-for", "markdown": "https://wpnews.pro/news/hypno-a-graph-based-neural-operator-with-physics-informed-message-passing-for.md", "text": "https://wpnews.pro/news/hypno-a-graph-based-neural-operator-with-physics-informed-message-passing-for.txt", "jsonld": "https://wpnews.pro/news/hypno-a-graph-based-neural-operator-with-physics-informed-message-passing-for.jsonld"}}