# ONE CYLinder: A Benchmark for Graph-Based Surrogate Modeling of Unsteady Bluff-Body Flows

arXiv: https://arxiv.org/abs/2609.08947 · HTML: https://mlsanity.com/paper/2609.08947/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 92 references that are in the map.
- First posted on arXiv 8 Sep 2026.

## Builds on (most cited first, 30 of 44)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
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- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Big Bird: Transformers for Longer Sequences](https://mlsanity.com/paper/2007.14062/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [Graph Neural Networks with Learnable Structural and Positional Representations](https://mlsanity.com/paper/2110.07875/) (2021)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [GPT-GNN: Generative Pre-Training of Graph Neural Networks](https://mlsanity.com/paper/2006.15437/) (2020)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries](https://mlsanity.com/paper/2502.02414/) (2025)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Gated Graph Recurrent Neural Networks](https://mlsanity.com/paper/2002.01038/) (2020)
- [Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers](https://mlsanity.com/paper/2302.10803/) (2023)
- [CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics](https://mlsanity.com/paper/2310.05963/) (2023)
- [Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN](https://mlsanity.com/paper/2210.02573/) (2022)
- [EfficientTrain: Exploring Generalized Curriculum Learning for Training Visual Backbones](https://mlsanity.com/paper/2211.09703/) (2022)

## Abstract (arXiv)

Graph-based surrogate models offer a promising route to accelerate computational fluid dynamics (CFD) simulations on unstructured meshes. However, their development is limited by the scarcity of benchmark datasets spanning multiple flow regimes and standardized protocols for long-horizon autoregressive prediction. We introduce ONECYL (ONE CYLinder), a new benchmark for unsteady flow past a circular cylinder across laminar, transitional, and high-Reynolds-number regimes. The benchmark comprises 450 high-fidelity Variational Multiscale finite-element simulations (270,000 flow snapshots) with randomized cylinder geometries, providing time-resolved velocity and pressure fields together with mesh connectivity, geometric descriptors, Reynolds numbers, and integrated aerodynamic quantities. Beyond the dataset, ONECYL establishes a unified evaluation framework combining full-field rollout errors, virtual probes, and drag and lift predictions to assess numerical accuracy and physical fidelity. To accompany the benchmark, we develop a Graph Transformer as a reference baseline predicting velocity and pressure fields autoregressively on unstructured meshes. Using ONECYL, we investigate geometric representations and physics-based regularization across the three Reynolds-number regimes. The results show that explicitly encoding the cylinder geometry through a level-set representation consistently improves long-horizon prediction accuracy and generalization to unseen geometries, while divergence-based regularization becomes increasingly beneficial as flow complexity increases. The ONECYL benchmark and its Graph Transformer baseline provide a reproducible framework for evaluating graph-based surrogate models and establish a foundation for future research on long-horizon prediction of unsteady bluff-body flows.