---
title: 'SuperWing: A 3D Transonic Wing Dataset'
url: https://www.emergentmind.com/topics/superwing
type: topic
---

# SuperWing: A 3D Transonic Wing Dataset

SuperWing is a large-scale, open-access dataset of three-dimensional transonic swept-wing aerodynamics designed to support the development of machine-learning surrogates for aerodynamic prediction. The dataset comprises 4,239 parameterized wing geometries and 28,856 steady Reynolds-averaged Navier-Stokes (RANS) flow field solutions, each simulated using the Spalart–Allmaras turbulence model at a fixed Reynolds number of $2 \times 10^7$ over Mach numbers in $[0.75, 0.90]$ and angles of attack in $[2^\circ, 12^\circ]$. SuperWing’s expansive geometric diversity and standardized mesh format are tailored for pre-training neural surrogates, foundation-model workflows, and generalizable aerodynamic modeling tasks [2512.14397, 2604.18062, 2605.05586].

## 1. Purpose, Scope, and Motivation

SuperWing was constructed to address the data scarcity and geometric homogeneity limiting generalizable surrogate modeling in three-dimensional wing aerodynamics. Existing datasets concentrate on minor perturbations of a baseline wing or restricted planform variations, impairing transfer and generalization to new designs. SuperWing systematically spans the design space of transport-class swept wings using well-parameterized, realistic geometry families and broad aerodynamic conditions.

Its primary objectives are:
- To serve as a pre-training corpus for neural surrogates (e.g., ViT, AeroTransformer, AeroJEPA) that can be cheaply fine-tuned on scarce, downstream cases.
- To enable foundation-model approaches in aerodynamic prediction, supporting interactive design, zero-shot generalization to unseen configurations, and multi-objective optimization workflows [2604.18062].
- To support machine learning research into continuous surrogate modeling, latent-design interfaces, and generalization across broad aerodynamic regimes [2605.05586].

## 2. Wing Geometry Parameterization

SuperWing parameterizes each wing using a combination of global planform and spanwise-varying geometric controls. The core features are:

- **Planform Parameters (5 total):**
  - Leading-edge sweep, $\Lambda_{\mathrm{LE}} \in [25^\circ, 40^\circ]$
  - Aspect ratio, $AR \in [8, 11]$
  - Taper ratio, $TR \in [0.15, 0.40]$
  - Kink location, $\eta_k \in [0.36, 0.42]$ (fraction of semi-span)
  - Root chord adjustment, $\kappa_{\mathrm{root}} \in [0.10, 1.10]$

- **Spanwise Distributions:**  
  Airfoil, twist, and dihedral are each described by splined parameters:
  - Airfoil shape at each spanwise station is generated from a baseline using the Class-Shape Transformation (CST) method with 20 coefficients (10 per surface), controlling upper and lower shapes:
    $$
    C_{\text{shape}}(\xi) = \sum_{i=0}^n C_i \, \xi^i (1 - \xi)^{n-i}
    $$
    where $\xi$ is normalized chordwise position.
  - Thickness and camber are modulated by B-spline functions with 5 control points per mode.
  - Dihedral is varied with two spline points (kink, tip).
  - Geometric twist is set using a 5-point spanwise spline.

- **Total Parameterization:**  
  The complete geometry vector consists of 37–54 parameters, depending on dataset version, encompassing planform, airfoil, dihedral, and twist (see details in [2512.14397, 2605.05586]). This parameterization permits realistic, non-trivial morphologies—avoiding reliance on single-wing perturbations.

## 3. CFD Simulation Protocol and Dataset Structure

- **CFD Setup:**  
  All cases are steady RANS (Spalart–Allmaras turbulence closure) at $T_\infty = 300$ K and $Re = 2 \times 10^7$, spanning:
  - Mach: $0.75 \leq Ma \leq 0.90$
  - Angle of attack: $2^\circ \leq \alpha \leq 12^\circ$
- **Mesh and Surface Representation:**  
  Each wing is resolved on a high-fidelity structured mesh (typ. $256 \times 128$ grid points for learning, $\sim$32,000 unstructured points for point-cloud experiments). Surface meshes use right-handed coordinates ($x$ downstream, $y$ spanwise, $z$ normal).

- **Flow Outputs:**
  - Surface pressure coefficient, $C_p$ ($\mathbb{R}^{256 \times 128}$ or as a point cloud).
  - Surface friction vector, $C_f$ ($\mathbb{R}^{256 \times 128 \times 2}$), decomposed as streamwise ($C_{f, \tau}$) and spanwise ($C_{f, z}$).
  - Integrated aerodynamic coefficients ($C_L$, $C_D$, $C_{M, z}$) are also provided per sample.

- **Operating Conditions:**
  - Each wing is evaluated at up to eight $(Ma, \alpha)$ pairs, resulting in mean coverage of 6.8 conditions per geometry.

- **Data Organization and Files:**  
  Samples are packaged as NumPy (.npy/.npz) or HDF5 for efficient batch loading. Each sample contains:
    - `coords.npy` – $(256,128,3)$ coordinates
    - `Cp.npy` – $(256,128)$ pressure
    - `Cf.npy` – $(256,128,2)$ friction vector
    - `cond.json` – Mach, AoA
    - `coefs.json` – integrated coefficients
  A global index lists all cases along with geometry parameters [2512.14397, 2604.18062].

## 4. Statistical Diversity and Dataset Splits

- **Diversity and Intrinsic Dimension:**
  - 4,239 unique planform/airfoil/twist/dihedral combinations, with continuous uniform sampling across parameter ranges.
  - Principal component analysis (PCA) indicates 5 modes explain 99% of shape variance, 11 for 99.9%—demonstrating dimensional regularity yet sufficient complexity for generalization studies.
  - No explicit data augmentation applied; diversity arises solely from the parameter sampling.
- **Splitting and Coverage:**  
  - Standard split: 90% for training, 10% for held-out evaluation with splits by geometry (no cross-leakage).
  - Some studies use 80/10/10 splits (train/val/test) by geometry.
  - Validation sets are extracted from training during model selection.

## 5. Machine Learning Benchmarks and Generalization Tests

SuperWing supports rigorous benchmarking for high-capacity surrogates:

- **Architectures:**
  - U-Net, Vision Transformer (ViT), Transolver, Point-cloud transformers (AeroJEPA).
- **Input Modalities:**
  - Structured mesh (coords, operating conditions).
  - Unstructured surface point cloud (for point-cloud networks).
- **Target Outputs:**
  - Surface fields $C_p$, $C_{f, \tau}$, $C_{f, z}$ and integrated coefficients.
- **Training Details:**
  - Mean squared error loss on fields, Adam/AdamW optimizers, batch sizes 4–32; standard normalization/centering as preprocessing.
- **Representative Benchmark Results ([2512.14397]):**

| Model      | $C_p$ err (%) | $C_{f, \tau}$ (%) | $C_{f, z}$ (%) | $C_L$ ($10^{-3}$) | $C_D$ ($10^{-4}$) | Time (h) | Mem (GB) |
|------------|---------------|-------------------|----------------|-------------------|-------------------|----------|----------|
| U-Net      | 1.101         | 0.642             | 0.698          | 23.41             | 14.78             | 17.1     | 5.55     |
| ViT        | 0.329         | 0.245             | 0.281          | 2.76              | 2.48              | 12.6     | 5.78     |
| Transolver | 0.359         | 0.271             | 0.310          | 2.71              | 2.53              | 37.9     | 16.42    |

ViT exhibits the best surface and global aerodynamic accuracy (e.g., 2.48 drag-count error) with low memory and wall time.

- **Zero-Shot Generalization:**
  - ViT pretrained on SuperWing matches CRM and DLR-F6 benchmark wings without fine-tuning, reproducing surface shocks and global $C_L$, $C_D$ curves.
  - Out-of-distribution (OOD) predicted error in drag-counts remains comparable to in-domain test error (2–4 counts).
- **Latent-Space Surrogates:**
  - AeroJEPA learns geometry- and condition-encoded latent predictions, supporting scalable field reconstruction and smooth latent optimization [2605.05586].

## 6. Practical Use and Integration

- **Loading and Preprocessing:**
  - Mesh coordinates are normalized by root chord length ($c_\text{root}=1.0$), centered at the origin.
  - Surface field outputs are standardized to $[-1,1]$ based on training set extrema.
  - Provided Python loaders (PyTorch Dataset, etc.) enable direct ingestion into training loops.

```python
class SuperWingDataset(torch.utils.data.Dataset):
    def __getitem__(self, i):
        coords = np.load(path_to_coords[i])
        cond   = load_json(cond_path[i])
        Cp     = np.load(path_to_Cp[i])
        Cf     = np.load(path_to_Cf[i])
        return dict(coords=torch.FloatTensor(coords), cond=torch.FloatTensor([Ma, AoA]),
                    Cp=torch.FloatTensor(Cp), Cf=torch.FloatTensor(Cf))
```

- **Augmentation:**
  - No baseline augmentation; optional noise, twist, or dihedral perturbations can be layered for regularization if desired.
  - Structured mesh shape ensures simple batching—collation is row-wise stacking.

- **Foundation-model and Interactive Scenarios:**
  - Pretrained models can be fine-tuned on new domains using $\ll$1,000 cases.
  - Interactive design tools and downstream co-optimization frameworks leverage standardized format and open-access pre-trained weights [2604.18062].

## 7. Impact and Research Directions

SuperWing enables research in:
- Pretraining large-scale, generalizable 3D aerodynamic surrogates for design automation and iterative optimization.
- Studying latent representations that support controllable interpolation, design-variable probing, and "CAD-free" gradient-based optimization [2605.05586].
- Benchmarking scalable architectures and zero-shot transfer, with evidence that ViT and AeroJEPA capture regime-crossing generalization.
- Supporting workflows for generative aerodynamic shape design, surrogate-assisted co-optimization, and rapid evaluation in architecture screening and conceptual design.
- Future directions include extension to unsteady flows, multi-point flight envelopes, and integration with multi-modality structural models [2512.14397, 2605.05586].

SuperWing’s expansive geometric coverage and rigorously standardized data modalities position it as a reference benchmark for aerodynamic surrogate model research as well as practical tools for data-driven wing design.

Source: https://www.emergentmind.com/topics/superwing