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AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions

Florent BonnetJocelyn Ahmed MazariPaola CinnellaPatrick Gallinari

article2022NeurIPS129 citations

Presents a high-fidelity dataset of Reynolds-Averaged Navier–Stokes simulations over 2D airfoils alongside specialized surface force evaluation metrics and deep learning benchmarks to standardize surrogate modeling for aerodynamic design.

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Engineering optimization in aerodynamics relies heavily on numerical simulations of fluid flow, but conventional computational methods are extremely time-consuming and resource-intensive. Running a single steady-state fluid simulation often takes thousands of computing hours, which severely limits the ability to rapidly explore and optimize wing designs. While fast machine learning surrogate models offer a potential alternative, progress in the field has been hindered by a lack of standardized, high-fidelity reference datasets and realistic evaluation protocols.

The article addresses this gap by introducing AirfRANS, an open-source, high-fidelity benchmark dataset designed to train and evaluate data-driven models for two-dimensional aerodynamic flows. The primary objective is to provide a rigorous standard for testing whether machine learning models can accurately approximate fluid flow fields and predict crucial aerodynamic forces under realistic flight conditions.

To construct the dataset, the researchers ran 1,000 high-resolution numerical simulations over diverse parameterized airfoil shapes under subsonic conditions, covering standard operational variations in flight speed and angles of attack. Each simulation utilized fine-scale computational meshes of 250,000 to 300,000 cells to precisely capture boundary-layer physics and surface forces. The article then established four distinct evaluation setups—full data, scarce data, speed extrapolation, and angle-of-attack extrapolation—and benchmarked several deep learning architectures capable of processing unstructured mesh data.

The key finding of the evaluation is that modern deep learning models predict aerodynamic lift with high reliability, achieving rank correlation scores above 0.90 across all models and reaching 0.965 with local graph neural networks. In stark contrast, all evaluated models failed to accurately predict aerodynamic drag, showing poor or negative rank correlations (such as -0.303 for graph neural networks) due to large velocity estimation errors very close to the airfoil surface. Furthermore, the experiments demonstrated that model performance degrades significantly when attempting to extrapolate beyond the training speeds or flight angles, whereas data scarcity during standard interpolation causes only minor performance drops. In terms of efficiency, training the surrogate models requires two to seven hours on a single graphics processing unit, amortizing the upfront computational investment after just a dozen full simulations and enabling subsequent flow predictions in fractions of a millisecond.

These findings imply that surrogate deep learning models are currently viable for rapid, early-stage lift estimation and shape ranking, delivering massive speedups that could accelerate design iterations and lower computational costs. However, engineering teams cannot yet rely on these models for full aerodynamic optimization, as calculating the lift-to-drag ratio remains compromised by inaccurate drag predictions. In practice, adopting surrogate models today requires combining them with traditional simulation solvers to cross-verify drag forces and guard against inaccurate extrapolations outside standard operating regimes.

Moving forward, development should focus on improving the prediction of boundary-layer velocity gradients and surface friction, incorporating physics-guided architectures, and expanding the benchmark toward complex three-dimensional flow phenomena. While the current results provide high confidence in the utility of surrogate modeling for subsonic lift prediction on standard airfoil geometries, decision-makers should maintain caution regarding drag estimates and unverified operating envelopes until more robust boundary-layer models are established.

incompressible flowAirfRANSReynolds-Averaged Navier-Stokes SolutionsComputational Fluid Dynamics Dataset
arXiv: 2212.07564Extrality/AirfRANS
Cover for AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions

Abstract

Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier–Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking. In this work, we develop AIRFRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier–Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study AIRFRANS under different constraints for generalization considerations: big and scarce data regime, Reynolds number, and angle of attack extrapolation.

Topics

incompressible flow

Keywords

AirfRANSReynolds-Averaged Navier-Stokes SolutionsComputational Fluid Dynamics DatasetGeometric Deep LearningTurbulence ModelingNACA airfoilsSST turbulencedrag coefficientCFD meshshape optimization

Table of Contents

  • 1 Introduction
  • 2 Related Work
  • 3 Dataset Presentation
  • 4 Benchmarking Setup
  • 5 Benchmarking Results
  • 6 Conclusion
  • References
  • 7 Paper Checklist

Knowls

  1. Knowl 1 — AIRFRANS high-fidelity aerodynamics dataset

    data/table

    AIRFRANS contains 1,000 high-fidelity steady-state simulations of two-dimensional incompressible Reynolds-Averaged Navier–Stokes flow around NACA 4- and 5-digit airfoils. Each simulation is specified by an airfoil geometry, a Reynolds number between 2 and 6 million, and an angle of attack between −5∘-5^\circ and 15∘15^\circ. The simulations represent subsonic flight at sea level and 298.15 K298.15\,\mathrm{K}, with Mach number below 0.30.3 and freestream velocity above 30 m s−130\,\mathrm{m\,s^{-1}}. Each sample provides an unstructured CFD mesh and solution fields for the mean velocity components, reduced pressure, and turbulent kinematic viscosity; drag and lift coefficients are computed from the solution as derived quantities. The dataset is intended for surrogate models that predict both spatial flow fields and design-relevant aerodynamic forces.

  2. Knowl 2 — Parameterized NACA airfoil design space

    data/table

    AIRFRANS samples airfoils from explicitly parameterized NACA 4- and 5-digit families. In a 4-digit sequence MPXXMPXX, MM is the maximum camber ordinate in hundredths of the chord, PP is the location of maximum camber in tenths of the chord, and XXXX is the maximum thickness in hundredths of the chord. In a 5-digit sequence LPQXXLPQXX, LL and PP determine the camber line, Q∈{0,1}Q\in\{0,1\} selects a single- or double-cambered profile, and XXXX again specifies thickness. One chord is 1 m1\,\mathrm{m}. Sampling is uniform over each interval or discrete set shown below; 4-digit values of PP below 1.51.5 are collapsed to P=0P=0 to avoid geometries whose maximum camber is too close to the trailing edge.

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  3. Knowl 3 — Incompressible RANS and turbulence model used for the simulations

    equation

    The CFD targets are steady ensemble-averaged solutions of the two-dimensional incompressible RANS equations with a turbulent-viscosity closure. For spatial coordinates (x1,x2)∈R2(x_1,x_2)\in\mathbb{R}^2, mean velocity components uˉi [m s−1]\bar u_i\,[\mathrm{m\,s^{-1}}], reduced pressure pˉ [m2 s−2]\bar p\,[\mathrm{m^2\,s^{-2}}], molecular kinematic viscosity ν [m2 s−1]\nu\,[\mathrm{m^2\,s^{-1}}], and turbulent kinematic viscosity νt [m2 s−1]\nu_t\,[\mathrm{m^2\,s^{-1}}], the equations are

    ∂iuˉi=0,\partial_i\bar u_i=0, ∂j(uˉiuˉj)=−∂ipˉ+(ν+νt)∂jj2uˉi,i∈{1,2}.\partial_j(\bar u_i\bar u_j)=-\partial_i\bar p+(\nu+\nu_t)\partial_{jj}^2\bar u_i,\qquad i\in\{1,2\}.

    Here ∂i=∂/∂xi\partial_i=\partial/\partial x_i, ∂jj2\partial_{jj}^2 denotes the sum of second derivatives over the repeated spatial index jj, and repeated indices are summed. The pressure is written in reduced form, so the density does not explicitly appear in the momentum equation. AIRFRANS closes the turbulent-viscosity dynamics with the kk–ω\omega SST turbulence model, selected for aerodynamic flows.

  4. Knowl 4 — High-resolution C-grid simulation generation

    experimental setup

    Each AIRFRANS airfoil is meshed with OpenFOAM v2112 blockMesh using a multi-block C-grid modeled after NASA NACA validation meshes. The outer boundaries are placed 200 chords from the airfoil to reduce boundary-condition effects. The boundary layer is highly resolved: the first cells adjacent to the airfoil have height 2 μm2\,\mu\mathrm{m}, giving approximately y+≈1y^+\approx1 in the worst case across the design space, and each mesh contains roughly 250,000–300,000 cells. The steady-state simulations use the OpenFOAM simpleFOAM solver with the SIMPLEC algorithm and the kk–ω\omega SST model, and run until the drag and lift coefficients converge on 16 CPU cores of an AMD Ryzen Threadripper 3960X. The mesh illustration on page 5 shows the C-shaped far field, the airfoil boundary, and the strongly refined near-wall region; the accompanying field visualization shows pressure and streamwise velocity around a sampled NACA airfoil.

  5. Knowl 5 — Postprocessed drag and lift coefficients

    equation

    The force on an airfoil combines pressure and viscous wall-shear contributions. Let DD be the component of force parallel to the freestream and LL the component perpendicular to it. With fluid density ρ [kg m−3]\rho\,[\mathrm{kg\,m^{-3}}], freestream velocity U∞ [m s−1]U_\infty\,[\mathrm{m\,s^{-1}}], and characteristic area A=1 m2A=1\,\mathrm{m^2} for the unit-chord two-dimensional airfoil, the dynamic pressure and dimensionless force coefficients are

    q∞=ρU∞2A2,CD=Dq∞,CL=Lq∞.q_\infty=\frac{\rho U_\infty^2A}{2},\qquad C_D=\frac{D}{q_\infty},\qquad C_L=\frac{L}{q_\infty}.

    The wall shear stress is obtained from the velocity gradient at the airfoil surface, evaluated numerically with the ParaView gradient filter. AIRFRANS does not directly regress the force coefficients: they are recomputed from the predicted velocity and pressure fields, with the surface velocity gradient supplying the viscous contribution.

  6. Knowl 6 — Four generalization tasks and data splits

    experimental setup

    The 1,000 simulations define four benchmark regimes. In the full-data regime, 800 simulations are used for training and 200 for testing. In the scarce-data regime, only 200 simulations are used for training, while the full-data regime's 200-example test set is retained. In Reynolds-number extrapolation, training uses samples with Reynolds numbers from 3 to 5 million, and testing uses the two held-out ranges from 2 to 3 million and from 5 to 6 million. In angle-of-attack extrapolation, training uses angles from −2.5∘-2.5^\circ to 12.5∘12.5^\circ, while testing uses the two tails, [−5∘,−2.5∘][-5^\circ,-2.5^\circ] and [12.5∘,15∘][12.5^\circ,15^\circ]. The regimes separate interpolation with abundant or scarce data from extrapolation in the physical operating conditions.

  7. Knowl 7 — Unstructured surrogate representation, sampling, and loss

    model/method

    The surrogate models regress four normalized fields at every mesh node: the two mean velocity components, reduced pressure, and turbulent kinematic viscosity. Before learning, each simulation is cropped to the rectangle [−2,4]×[−1.5,1.5][-2,4]\times[-1.5,1.5] metres and each field component is normalized using the training-set mean and standard deviation. At every epoch, 32,000 nodes are sampled uniformly from the cropped mesh; when a graph is required, a radius graph with radius 5 cm5\,\mathrm{cm} and at most 64 neighbours is constructed. A node input xi∈R7x_i\in\mathbb{R}^7 contains its two spatial coordinates, the inlet velocity, its Euclidean distance to the airfoil, and its outward surface normal; the normal is set to zero for volume nodes. A target yi∈R4y_i\in\mathbb{R}^4 contains velocity, pressure, and turbulent viscosity. For model fθf_\theta with parameters θ\theta, volume-node index set VV, surface-node index set SS, and balancing coefficient λ=1\lambda=1, training minimizes

    L=1∣V∣∑i∈V∥fθ(xi)−yi∥22+λ1∣S∣∑i∈S∥fθ(xi)−yi∥22.\mathcal{L}=\frac{1}{|V|}\sum_{i\in V}\lVert f_\theta(x_i)-y_i\rVert_2^2+\lambda\frac{1}{|S|}\sum_{i\in S}\lVert f_\theta(x_i)-y_i\rVert_2^2.

    At inference, multiple random 32,000-node passes cover the original mesh; predictions for nodes seen more than once are averaged. The original CFD mesh is then used with PyVista to calculate surface velocity gradients and force coefficients. The authors caution that this loss is not necessarily a proxy for accurate wall shear stress or exact satisfaction of the RANS equations.

  8. Knowl 8 — Design-oriented evaluation protocol

    model/method

    AIRFRANS evaluates both field reconstruction and aerodynamic usefulness. Quantitative field metrics are mean squared error on the volume and on the airfoil surface for each regressed field. Force metrics are the mean and standard deviation of the relative errors in CDC_D and CLC_L, together with Spearman rank correlations ρD\rho_D and ρL\rho_L between predicted and true coefficients. Spearman correlation is central for shape optimization because a value near one indicates that a surrogate preserves the ordering of candidate airfoils even if its absolute force values are biased. Qualitative evaluation consists of boundary-layer profiles for velocity and turbulent viscosity, surface pressure and skin-friction coefficients, and predicted-versus-true force-coefficient plots. The paper proposes a hierarchy in which rank correlation is the primary design metric, force relative error is secondary, and field MSE measures accuracy; a relative-error threshold of 5% is noted as a commonly used indication of sufficient force accuracy.

  9. Knowl 9 — Graph and point-cloud baseline comparison

    experimental setup

    The full-data benchmark compares an MLP, GraphSAGE, PointNet, and Graph U-Net. Every model is preceded by an MLP encoder and followed by an MLP decoder, and each is trained five times so reported values are means with standard deviations. The MLP uses only node features; GraphSAGE additionally uses local neighbourhoods; PointNet conditions node processing on global point-cloud features; and Graph U-Net uses multi-scale local-to-global graph information. All models use the same preprocessing, node sampling, loss, and test protocol.

  10. Knowl 10 — Field and force performance in the full-data regime

    data/table

    The following results are means ±\pm standard deviations over five training runs on the full-data test set. Field values are MSEs on normalized predictions; the four volume columns are scaled by 10−210^{-2} and the surface-pressure column by 10−110^{-1}. Force relative errors and Spearman correlations are computed after reconstructing CDC_D and CLC_L from the unnormalized predicted fields. The results show a division of strengths: Graph U-Net gives the best surface-pressure MSE and lift relative error, while GraphSAGE gives the best streamwise-velocity and volume-pressure MSEs. All models have poor drag rank correlation, whereas lift rank correlation is high.

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    Could not parse LaTeX table

    The authors attribute the drag failure to overestimated near-wall velocities and consequently inaccurate wall shear stress. Lift is easier because its dominant surface-pressure contribution is predicted more accurately. GraphSAGE is presented as a practical compromise: it has near-Graph-U-Net performance, approximately half as many parameters, and is almost twenty times faster per inference call.

  11. Knowl 11 — Scarcity and physical extrapolation results

    data/table

    GraphSAGE was evaluated on all four task regimes. The entries below are means ±\pm standard deviations; field quantities are normalized MSEs, with the scaling factors shown in the first column, and force quantities are relative errors or Spearman correlations. The extrapolation test sets differ from the interpolation test set, so values across regimes should be interpreted as task-specific difficulty indicators rather than perfectly matched comparisons.

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    More data improves interpolation field accuracy: the scarce regime has larger field MSEs than the full regime. However, its force errors are not uniformly worse, illustrating that field MSE is not a reliable proxy for integrated force accuracy because local errors can accumulate or cancel on the surface. Reynolds and angle-of-attack extrapolation substantially degrade field accuracy. Lift rank correlation remains useful but falls from 0.9650.965 in the full regime to 0.9270.927 for Reynolds extrapolation and 0.9080.908 for angle-of-attack extrapolation; drag rank correlation remains close to zero in every regime.

  12. Knowl 12 — Computational cost and amortization

    data/table

    The CFD data-generation cost is much higher than surrogate inference. The following measurements use 16 CPU cores of an AMD Ryzen Threadripper 3960X for simulation and an NVIDIA GeForce RTX 3090 for model training and inference. Inference time is for one 32,000-node model call; approximately 100 such calls are needed to cover one full CFD mesh through random subsampling. The dataset required approximately 20 days to generate, whereas one CFD simulation required approximately 25 minutes.

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    The authors conclude that even for this two-dimensional problem, surrogate training becomes cost-effective after roughly a dozen CFD simulations in the worst case, because the trained model can be queried much faster than solving a new RANS system.

  13. Knowl 13 — Scope and methodological limitations

    limitation

    The dataset restricts geometry to NACA 4- and 5-digit airfoils to simplify parameterization and automated meshing; models trained on AIRFRANS are therefore expected to have difficulty with more exotic, out-of-distribution shapes, and the benchmark does not test shape extrapolation. The flow is two-dimensional, so success on AIRFRANS does not establish applicability to generic three-dimensional fluid phenomena. Graph models are computationally heavy on the large CFD graphs and require downsampling; because the complete graph is supplied as input, automatic differentiation with respect to node positions is not available, so surface derivatives must be computed numerically on the original CFD mesh. Conversely, MLPs avoid this graph and derivative restriction but generally need additional conditioning or hypernetwork mechanisms to generalize across multiple simulations. Finally, the regression loss is not guaranteed to enforce the RANS equations or accurately reproduce wall shear stress, which is reflected in the weak drag predictions.

Coverage note — Detailed appendix-only boundary conditions, constants, architecture hyperparameters, and individual qualitative boundary-layer plots were omitted because they operationalize the released benchmark or repeat the summarized evaluation and results rather than constitute separate load-bearing contributions.

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Citation

MLA
Bonnet, F., et al. “AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions”. 36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks, 2022, http://arxiv.org/abs/2212.07564v3.
APA
Bonnet, F., Mazari, A. J., Cinnella, P., & Gallinari, P. (2022). AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions. 36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks. http://arxiv.org/abs/2212.07564v3
Chicago
Bonnet, F., A. J. Mazari, P. Cinnella, and P. Gallinari. 2022. “AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions”. 36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks. http://arxiv.org/abs/2212.07564v3.
Harvard
Bonnet, F. et al. (2022) “AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions”, 36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks [Preprint]. Available at: http://arxiv.org/abs/2212.07564v3.
Vancouver
1. Bonnet F, Mazari AJ, Cinnella P, Gallinari P (2022) AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions. 36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks

BibTeX

@article{bonnet2022airfrans,
  title = {AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions},
  author = {Bonnet, Florent and Mazari, Ahmed Jocelyn and Cinnella, Paola and Gallinari, Patrick},
  year = {2022},
  journal = {36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks},
  url = {http://arxiv.org/abs/2212.07564v3},
  eprint = {2212.07564}
}
Metadata:arXiv

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