# Hyperbolic Neural Operator (HNO)

> ICML 2026 paper on Lorentz-distance attention for multiscale PDE operator learning, by Jieyuan Pei, Zhuoxuan Li, Wei Li, Haobo Zhang, Jiawei Jiang, Jianwei Zheng.

HNO uses hyperbolic latent geometry to organize near–far interactions. Evaluated tasks include Elasticity, Navier–Stokes, Darcy, Plasticity, Airfoil, Pipe, AirfRANS and ShapeNet Car.

## Paper
- [Abstract, research summary and results](https://guobapei.github.io/Hyperbolic-Neural-Operator/paper.html): Contributions, benchmark values, comparison conditions and citation.
- [Original paper PDF](https://guobapei.github.io/Hyperbolic-Neural-Operator/assets/paper.pdf): Author-provided 59-page manuscript with figures, equations, references and appendix.
- [Complete paper as plain text](https://guobapei.github.io/Hyperbolic-Neural-Operator/paper.txt): Text extracted from the PDF.
- [Complete paper as HTML](https://guobapei.github.io/Hyperbolic-Neural-Operator/fulltext.html): Extracted text with links to original PDF pages.
- [Markdown research summary](https://guobapei.github.io/Hyperbolic-Neural-Operator/summary.md): Abstract, method overview, benchmark table and citation.

## Citation and code
- [BibTeX](https://guobapei.github.io/Hyperbolic-Neural-Operator/citation.bib): Conference citation.
- [Structured paper metadata](https://guobapei.github.io/Hyperbolic-Neural-Operator/paper.json): Schema.org ScholarlyArticle metadata.
- [Official code](https://github.com/GuobaPei/Hyperbolic-Neural-Operator): Models, training scripts and quick start.
- [OpenReview](https://openreview.net/forum?id=CUQwYTTNu8): Conference review record.
- [ICML](https://icml.cc/virtual/2026/poster/65554): Official conference entry.