WebWing: Rapid Aerodynamic Predictions

• WebWing is an interactive, browser-based design tool that provides rapid, real-time aerodynamic predictions for 3D transonic wings.
• It leverages the AeroTransformer model, pre-trained on the diverse SuperWing dataset and fine-tuned on NASA CRM perturbations, to achieve high prediction accuracy.
• The tool replaces expensive CFD calculations with instantaneous visualizations of surface flows and aerodynamic coefficients, enabling fast early-stage design exploration.

WebWing is an interactive, browser-based design tool for rapid aerodynamic prediction of three-dimensional transonic wings. It is built on AeroTransformer, a large-scale transformer surrogate model pre-trained on the diverse “SuperWing” dataset and fine-tuned to detailed perturbations of the NASA Common Research Model (CRM). WebWing enables users to modify wing geometry and operating conditions via an intuitive web interface, performing real-time predictions of surface flow and aerodynamic coefficients, thus replacing computationally expensive CFD calculations during early-stage design exploration. The system exemplifies the foundation-model paradigm in engineering surrogate modeling, combining broad pre-training with targeted fine-tuning to achieve high accuracy and generalization (Yang et al., 20 Apr 2026).

1. AeroTransformer Surrogate Model Architecture

AeroTransformer extends the hierarchical PDE-Transformer backbone to map three-dimensional wing geometries and operating conditions to either surface-flow fields or integrated aerodynamic coefficients. Input wing geometries $g \in \mathbb{R}^{H \times W \times 3}$ are discretized on a structured mesh ($H=256$, circumferential; $W=128$, spanwise), with each mesh cell containing $(x, y, z)$ coordinates. These are embedded using a shared $4 \times 4$ convolutional “patching” layer, yielding $M = (H/4) \times (W/4)$ tokens.

Operating conditions $c \in \mathbb{R}^{N_c=2}$, specifically Mach number ($Ma$) and angle of attack ($\alpha$), are injected into every transformer block using adaptive layer normalization conditioning (“adaLN-Zero”). A small MLP projects $c$ to $H=256$0, from which scale-and-shift vectors $H=256$1 are regressed to modulate activations.

The transformer backbone is organized in a U-shaped, hierarchical structure—with two down-sampling stages, a latent stage, and two up-sampling stages—and incorporates skip connections. Down-sampling uses PixelUnshuffle convolutions to decrease resolution while doubling the hidden dimension; up-sampling reverses this with PixelShuffle. Windowed (8×8) multi-head self-attention (W-MSA) and shifted window-attention (SW-MSA) limit global attention for computational efficiency. Positional information is encoded via log-spaced relative position embeddings.

Surface-flow predictions ($H=256$2, $H=256$3) are output via a final convolutional expansion and reshaping layer. For integrated coefficients ($H=256$4), latent tokens are aggregated by attention pooling and projected via a fully connected layer. The multi-task training objective is

$H=256$5

with $H=256$6 balancing field and coefficient accuracy. $H=256$7 is a mean squared error (MSE) loss on predicted surface pressure and friction vectors; $H=256$8 is an MSE on integrated coefficients obtained from the predicted surface fields (Yang et al., 20 Apr 2026).

2. Training Strategy: SuperWing Pre-training and CRM Fine-tuning

WebWing’s surrogate accuracy is enabled by a two-stage training paradigm:

A. SuperWing Pre-training:

The model is first pre-trained on SuperWing, comprising 4,239 distinct transonic wing shapes (planform parameters sampled uniformly across $H=256$9, $W=128$0, $W=128$1, $W=128$2, $W=128$3). Sectional airfoils are parameterized via B-splines; dihedral and twist via control points. Each shape is simulated at eight operating points ($W=128$4, $W=128$5), yielding 28,856 RANS flow fields. Model sizes S/M/L ($W=128$6=$W=128$7) span $W=128$8 parameters (Yang et al., 20 Apr 2026).

B. CRM Fine-tuning:

Fine-tuning uses 288 CRM wing perturbations around the NASA CRM baseline. Each shape (parameterized by 7 spanwise sections, airfoils varied with 20 CST coefficients, dihedral $W=128$9, twist $(x, y, z)$0) is simulated at eight operating conditions. Subsets of 450 samples serve as fine-tuning budgets. Fine-tuning the L-size model for 5.6k steps (49 minutes) achieves substantial error reduction versus scratch training. Ten-fold cross-validation is conducted on the 450 samples (Yang et al., 20 Apr 2026).

3. Surrogate Modeling Formulation and Metrics

Given inputs $(x, y, z)$1, AeroTransformer predicts either:

• Surface flow $(x, y, z)$2 on the mesh, enabling downstream integration to coefficients.
• Directly, aerodynamic coefficients $(x, y, z)$3.

Key evaluation metrics:

• Pointwise surface errors (normalized MAE):

$(x, y, z)$4

• Aggregate surface flow error (SFE):

$(x, y, z)$5

• Coefficient errors (MAE):

$(x, y, z)$6

These metrics enable quantitative comparison to CFD and to other ML-based surrogates (Yang et al., 20 Apr 2026).

4. WebWing Interface and Prediction Pipeline

WebWing utilizes a JavaScript/Three.js frontend and a remote GPU backend hosting the pre-trained L-size AeroTransformer. Users can adjust:

• Global planform (sliders: $(x, y, z)$7, $(x, y, z)$8, $(x, y, z)$9, $4 \times 4$0, $4 \times 4$1)
• Spanwise control points (airfoil CST coefficients, dihedral, twist at 7 stations) via drag handles or file upload
• Operating conditions (sliders: $4 \times 4$2, $4 \times 4$3)

Upon modification, the frontend serializes $4 \times 4$4 as JSON and sends it to the backend, which remeshes the geometry to a $4 \times 4$5 grid and executes AeroTransformer inference (∼30 ms for 9 conditions, on NVIDIA A5000). Predictions (surface $4 \times 4$6, $4 \times 4$7, $4 \times 4$8, $4 \times 4$9, $M = (H/4) \times (W/4)$0) are returned and visualized instantaneously:

• Interactive 3D coloring by $M = (H/4) \times (W/4)$1 or $M = (H/4) \times (W/4)$2
• Sectional 2D plots of $M = (H/4) \times (W/4)$3 vs. chordwise location
• Numeric display of integrated coefficients
• Real-time response on all user actions

This provides a rapid design loop that obviates hours of CFD per geometry (Yang et al., 20 Apr 2026).

5. Quantitative Performance and Comparative Analysis

The table below summarizes selected surrogate error metrics:

Method & Data Regime	SFE (%)	$M = (H/4) \times (W/4)$4	$M = (H/4) \times (W/4)$5
U-Net (SuperWing test, S)	0.911	–	–
ViT (SuperWing test, S)	0.353	–	–
Transolver (SuperWing test, S)	0.401	–	–
AeroTransformer S (SuperWing test)	0.279→0.264	2.35	2.11
From scratch (CRM 450, L)	1.00	38.1	27.9
Zero-shot pretrain (CRM 450, L)	0.376	14.7	8.87
Fine-tuned (CRM 450, L)	0.159	4.06	3.36
Attn-only finetune (15% params)	0.465	–	–
LoRA finetune (1.7% params)	0.499	–	–

Fine-tuning on 450 CRM samples achieves SFE=0.159% (a reduction of 84.2% vs. training from scratch), with inference times of ∼30 ms per geometry × 9 conditions. This outperforms baseline surrogates and reduces costs relative to RANS CFD, which requires hours per case. Parameter-efficient fine-tuning (attention layers or LoRA) yields only slight accuracy penalties (Yang et al., 20 Apr 2026).

6. Practical Usage, Limitations, and Case Studies

Recommended deployment involves two workflows: (1) zero-shot mode for rapid broad surveys in geometry/condition space, and (2) fine-tuning with a limited set of high-fidelity CRM-like samples when increased local accuracy ($M = (H/4) \times (W/4)$60.2% SFE) is required.

A documented case study involving CRM at $M = (H/4) \times (W/4)$7, $M = (H/4) \times (W/4)$8 demonstrates that both zero-shot and fine-tuned AeroTransformer predictions capture surface shock location, $M = (H/4) \times (W/4)$9 distribution, and polar curves within approximately $c \in \mathbb{R}^{N_c=2}$0 error on $c \in \mathbb{R}^{N_c=2}$1. This enables rapid cruise and off-design exploration.

Limitations are as follows:

• The SuperWing pre-training dataset is limited to single-airfoil-derived sectional shapes; extreme camber or novel planforms may degrade zero-shot accuracy.
• Fine-tuning is validated near CRM-derived perturbations; significant planform changes require further targeted data.
• The approach models surface flow only; volumetric (off-surface) effects are not addressed.

This suggests that while WebWing offers robust surrogate modeling for standard and moderate wing variations, further generalization to exotic geometries would require additional pre-training or domain adaptation (Yang et al., 20 Apr 2026).

7. Broader Context and Foundation-Model Paradigm

WebWing exemplifies the application of the foundation-model paradigm to aerodynamic design: large-scale diversity pre-training, followed by rapid, targeted adaptation via fine-tuning. By integrating advanced architectures with efficient surrogate modeling, WebWing provides near-CFD accuracy and substantially reduced response times, directly impacting early-stage design workflows in computational aerodynamics. The adaptive conditioning, hierarchical modeling, and real-time interactivity represent a substantial convergence of machine learning, engineering domain knowledge, and web-based design tools (Yang et al., 20 Apr 2026).