ONE CYLinder: A Benchmark for Graph-Based Surrogate Modeling of Unsteady Bluff-Body Flows
Authors: Théodore Michel, Antoine Campos, Alban Dujardin, Henry Areiza, Philippe Meliga, Elie Hachem
Organizations: Mines Paris PSL University Centre for Material Forming (CEMEF) UMR CNRS, Sophia Antipolis, 06904, France
Abstract
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.
A flow surrogate validated on a simple regime is often taken as evidence that the approach will carry to a richer one. We test this assumption on two transient flows under time-varying boundary conditions emulating the process startup: the three-dimensional slurry film in chemical-mechanical planarisation (CMP), a core semiconductor-manufacturing process, and the two-dimensional Karman vortex street (KVS) behind a cylinder. Eight surrogate models are compared on one shared evaluation pipeline, differing in whether they learn the full field or a latent representation, and whether they predict trajectories in one shot or step by step. No single architecture wins both regimes. On the film, a one-shot full-field model reconstructs the process-relevant cumulative wall shear stress to 3.2% relative error. On the wake, a latent autoregressive DeepONet retains 96% of the shedding power that direct and one-shot models damp to almost zero. The deciding axis is the treatment of time. The self-sustained wake requires the phase memory that autoregressive feedback provides, while the boundary-driven film rewards a direct map. Pointwise RMSE picks the wrong model in both regimes, so the evaluation scores five physical questions instead, the field, its structure, invented motion, amplitude, and timing. The trained surrogates answer queries 103 to 104 times faster than the finite-element solver, but the offline cost of the training simulations means they pay off from the first query beyond the training set for CMP and the third for the KVS. The choice of surrogate should follow the dynamical character of the target flow, and its validation should use failure-mode-resolved metrics, since neither the winning architecture nor its validation transfers.
Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical bottleneck in the field: while architectures have advanced significantly, the common underlying training paradigms remain bound to naive assumptions, such as node-wise supervision and explicit Euler time-stepping. These legacy choices ignore the stiff dynamics and local flux continuity inherent to numerous partial differential equations resolution methods, such as Finite Element, Difference, or Volume (FEM). In this work, we propose a unified framework to bridge the gap between geometric deep learning and rigorous numerical analysis. We introduce three key innovations: (1) Multi Node Prediction, a stencil-level objective that predicts field values for a node's full local topology, enforcing spatial derivative consistency; (2) Temporal Correction, replacing unstable explicit schemes with a predictor-corrector via temporal Cross-Attention; and (3) Geometric Inductive Biases, leveraging 3D Rotary Positional Embeddings (RoPE) to robustly capture rotational symmetries in unstructured meshes. We evaluate this framework across three architectures (MeshGraphNet, Transolver, and a Transformer) on diverse physics datasets. Our approach yields consistent improvements in accuracy and stability, particularly in long-horizon rollouts, while producing latent representations that generalize to unseen subtasks such as Wall Shear Stress or Pressure prediction. Code is available at https://github.com/DonsetPG/graph-physics.
Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field reconstruction in real-world flow benchmarks. The proposed formulation combines hybrid Fourier-wavelet spectral encoding with physics-biased self-attention based on partial differential equation residual diagnostics. It also uses self-supervised pretraining through Masked Physics Prediction and Equation Consistency Prediction. The experiments are conducted on two real benchmark cases: cylinder-wake flow and fluid-structure interaction. All approaches are evaluated under a shared local protocol and compared with spectral, transformer-based, operator-learning, and physics-informed neural-network baselines. On the cylinder-wake benchmark, the proposed model achieves the best aggregate accuracy, with an all-channel normalized mean-squared error of 0.05875 and an all-channel Pearson correlation coefficient of 0.97019. On the fluid-structure-interaction benchmark, it gives the lowest all-channel normalized mean-squared error of 2.70×10−4, compared with 4.02×10−4 for the strongest baseline. Component-wise field comparisons and scale-separated diagnostics further show stronger recovery of localized wake structures, including near-body, wake-core, and far-wake features. The results demonstrate improved real-world flow reconstruction while maintaining a practical accuracy-cost tradeoff.