Large Wing Model (LWM) Overview

• Large Wing Model (LWM) is a probabilistic machine-learning framework that predicts finite-wing pressure distributions and lift from sparse experimental data.
• It employs a modified deep kernel learning architecture with a neural feature map and Gaussian Process to capture geometric inputs and spanwise effects with uncertainty quantification.
• The model integrates a physics-driven prior from the Large Airfoil Model, improving data efficiency and enabling robust extrapolation for rectangular wings under attached flows.

Searching arXiv for the specified paper and closely related wing-model/dataset papers. arXiv search query: (Lee et al., 15 Aug 2025) Large Wing Model; (Diniz et al., 14 Dec 2025) OptiWing3D; (Yang et al., 16 Dec 2025) SuperWing. Large Wing Model (LWM) is a probabilistic machine-learning framework for finite-wing aerodynamics that predicts three-dimensional pressure coefficient distributions, $C_p(x,y)$, from a small, strictly experimental data set and propagates predictive uncertainty to sectional lift $c_l(y)$ and total lift $C_L$ (Lee et al., 15 Aug 2025). In the paper titled "Large Wing Model" (Lee et al., 15 Aug 2025), the model is formulated as a modified deep kernel learning system in which a neural feature map embeds geometric and operating-condition inputs into a latent space, while a Gaussian Process (GP) models spanwise structure and uncertainty. The stated scope is rectangular or lightly tapered wings, low to moderate sweep, and attached, subcritical/transonic flows, with extrapolation aided by a physics-driven prior formed from two-dimensional pressure predictions produced by the Large Airfoil Model (LAM) (Lee et al., 15 Aug 2025).

1. Definition, scope, and nomenclature

Within the aerodynamic literature represented here, LWM denotes the "Large Wing Model" introduced for wing-surface pressure and lift prediction from experimental data (Lee et al., 15 Aug 2025). Its target outputs are the mean and uncertainty of upper- and lower-surface $C_p(x,y)$, together with the mean and uncertainty of sectional lift $c_l(y)$ and total lift $C_L$, optionally followed by posterior conditioning to enforce known probabilistic lift descriptions (Lee et al., 15 Aug 2025). The problem addressed is explicitly the prediction of three-dimensional pressure distributions over finite wings under data scarcity, including three-dimensional effects such as those induced by wing tip vortices (Lee et al., 15 Aug 2025).

The same acronym is used differently in other arXiv papers. In "Opus" (Fagnoni et al., 2024), LWM stands for "Large Work Model," a workflow-centric model for Business Process Outsourcing. In "LWM-Temporal" (Alikhani et al., 22 Feb 2026), LWM stands for "Large Wireless Models," a family of wireless-channel foundation models. This acronymal overlap is a recurrent source of confusion; in the aerodynamic sense, however, LWM refers specifically to the finite-wing probabilistic predictor in (Lee et al., 15 Aug 2025).

Despite the name, the aerodynamic LWM is not presented as a generic large-scale wing generator. It is presented as a computationally efficient wing $C_p$ prediction model that facilitates rapid exploration of the wing design space, with uncertainty-aware inference and explicit lift propagation from the predicted pressure field (Lee et al., 15 Aug 2025).

2. Input representation and geometric parameterization

The model predicts pressure at query points expressed through a three-dimensional coordinate transform. The physical chordwise coordinate satisfies $x \in [0,c(y)]$, with normalized coordinate $x/c \in [0,1]$. A conformal-mapping-inspired representation is then introduced through

$\theta = \cos^{-1}(x/c),$

a linearly mapped $c_l(y)$0, and $c_l(y)$1, together with the normalized semi-span coordinate $c_l(y)$2 (Lee et al., 15 Aug 2025). Upper and lower surfaces are distinguished by the sign of $c_l(y)$3, with $c_l(y)$4 on the upper surface and $c_l(y)$5 on the lower surface, while leading and trailing edges have periodic identifications in $c_l(y)$6 (Lee et al., 15 Aug 2025).

The physical input vector is $c_l(y)$7 (Lee et al., 15 Aug 2025). It contains 28 sampled $c_l(y)$8 values that encode the airfoil section geometry, operating conditions $c_l(y)$9 and $C_L$0, wing planform descriptors $C_L$1, taper ratio $C_L$2, leading-edge sweep $C_L$3, and the conformal query-point coordinates $C_L$4 and $C_L$5 (Lee et al., 15 Aug 2025). The spanwise coordinate $C_L$6 is intentionally excluded from the neural network input and is instead appended directly to the GP input so that the GP preserves spanwise topology and tip-boundary effects (Lee et al., 15 Aug 2025).

This representation defines a 15-dimensional active space. The neural feature map produces 14 latent variables,

$C_L$7

and the GP operates on $C_L$8 (Lee et al., 15 Aug 2025). The modeling scope reported in the paper is primarily rectangular wings with $C_L$9, low to moderate sweep $C_p(x,y)$0--$C_p(x,y)$1, and aspect ratios $C_p(x,y)$2--$C_p(x,y)$3, over angles of attack $C_p(x,y)$4 and Mach numbers $C_p(x,y)$5 (Lee et al., 15 Aug 2025).

3. Deep-kernel-learning architecture and physics-driven prior

The core architecture is a modified deep kernel learning model (Lee et al., 15 Aug 2025). The neural feature extractor has architecture

$C_p(x,y)$6

and its weights are learned jointly with GP hyperparameters by marginal likelihood maximization (Lee et al., 15 Aug 2025). On the probabilistic side, the GP prior is written as

$C_p(x,y)$7

with observations corrupted by noise

$C_p(x,y)$8

where the second term captures digitization and unreported additional noise (Lee et al., 15 Aug 2025).

The covariance structure is a product kernel over the 14 latent dimensions and the spanwise coordinate (Lee et al., 15 Aug 2025). Each latent dimension uses a Matérn-$C_p(x,y)$9 kernel, while the spanwise dimension uses a Matérn-$c_l(y)$0 kernel with spatially varying hyperparameters. The spanwise hyperparameters are blended through a logistic transition,

$c_l(y)$1

with calibrated values $c_l(y)$2 and $c_l(y)$3 (Lee et al., 15 Aug 2025). The spanwise length scale $c_l(y)$4 decreases from approximately $c_l(y)$5 inboard to approximately $c_l(y)$6 outboard, while the signal variance changes slightly from approximately $c_l(y)$7 to approximately $c_l(y)$8 (Lee et al., 15 Aug 2025). The stated purpose of this nonstationarity is to allow the model to represent localized distortions near the tip, including trailing-edge pressure undulations associated with tip vortices (Lee et al., 15 Aug 2025).

A distinctive component is the physics-driven prior supplied by the Large Airfoil Model (Lee et al., 15 Aug 2025). LAM provides a probabilistic two-dimensional airfoil pressure distribution, and the LWM prior is formed by averaging LAM posteriors at four angles

$c_l(y)$9

thereby spanning the geometric angle of attack to $C_L$0 (Lee et al., 15 Aug 2025). The three-dimensional wing pressure field is then modeled as

$C_L$1

where $C_L$2 is a latent-space GP residual (Lee et al., 15 Aug 2025). The paper attributes several practical effects to this prior: reduced posterior variance, especially near the trailing edge; elimination of non-physical loops; and strong extrapolation across unseen airfoil sections (Lee et al., 15 Aug 2025).

4. Pressure, lift, uncertainty, and posterior conditioning

The aerodynamic outputs follow standard nondimensional definitions. The pressure coefficient is

$C_L$3

the sectional lift coefficient at spanwise station $C_L$4 is

$C_L$5

and the total wing lift coefficient is

$C_L$6

For rectangular wings, this reduces under $C_L$7 to

$C_L$8

(Lee et al., 15 Aug 2025).

The model produces posterior mean and variance through the usual GP predictive equations. With covariance matrices $C_L$9, $C_p$0, and $C_p$1 and noise covariance $C_p$2, the posterior mean and variance are

$C_p$3

with numerically stable Cholesky forms used in practice (Lee et al., 15 Aug 2025).

Uncertainty propagation to $C_p$4 and $C_p$5 is not performed analytically in the final system because the nonlinear feature map $C_p$6 breaks linear-Gaussian closure (Lee et al., 15 Aug 2025). Instead, the paper uses Monte Carlo propagation: it draws $C_p$7 samples from the full posterior predictive distribution of $C_p$8, integrates each sample chordwise to obtain $C_p$9, integrates spanwise to obtain $x \in [0,c(y)]$0, and then computes sample means, variances, and $x \in [0,c(y)]$1 confidence intervals as $x \in [0,c(y)]$2 under approximate Gaussianity of aggregated outputs (Lee et al., 15 Aug 2025).

An additional mechanism constrains the posterior predictive space when a target lift distribution is known. If, for example,

$x \in [0,c(y)]$3

the paper applies rejection sampling with acceptance probability

$x \in [0,c(y)]$4

where $x \in [0,c(y)]$5 is the empirical proposal derived from unconditioned posterior samples and $x \in [0,c(y)]$6 normalizes the ratio (Lee et al., 15 Aug 2025). The stated effect is reduced variance in $x \in [0,c(y)]$7 and $x \in [0,c(y)]$8, together with improved pressure predictions consistent with integrated lift constraints (Lee et al., 15 Aug 2025).

5. Experimental database, validation, and computational characteristics

The training database compiled for LWM comprises 16 unique wings, 54 operating conditions, and 23,723 individual pressure measurements (Lee et al., 15 Aug 2025). The wing airfoils include NACA 0012, 0015, 0023, RAE 101, NACA 64A-105, a 5% thick supercritical airfoil, and a "NACA 6-series-like" profile (Lee et al., 15 Aug 2025). Source data were gathered from government reports, technical notes, and papers, with tables extracted via OCR using ExtractTable and graphs digitized with WebPlotDigitizer; the resulting data were added to ASPIRE and released with code repositories for the Large Wing Model and Large Airfoil Model (Lee et al., 15 Aug 2025).

Three rectangular-wing test cases are reported (Lee et al., 15 Aug 2025). For a NACA 0012 wing at $x \in [0,c(y)]$9, $x/c \in [0,1]$0, and $x/c \in [0,1]$1, the model achieved $x/c \in [0,1]$2, $x/c \in [0,1]$3, and $x/c \in [0,1]$4 versus an experimental value of $x/c \in [0,1]$5, corresponding to $x/c \in [0,1]$6 error (Lee et al., 15 Aug 2025). For a second NACA 0012 case at $x/c \in [0,1]$7, $x/c \in [0,1]$8, and $x/c \in [0,1]$9, it achieved $\theta = \cos^{-1}(x/c),$0, $\theta = \cos^{-1}(x/c),$1, with predicted $\theta = \cos^{-1}(x/c),$2 and no reference value available (Lee et al., 15 Aug 2025). For a NACA 0015 wing excluded from training, at $\theta = \cos^{-1}(x/c),$3, $\theta = \cos^{-1}(x/c),$4, and $\theta = \cos^{-1}(x/c),$5, it achieved $\theta = \cos^{-1}(x/c),$6, $\theta = \cos^{-1}(x/c),$7, and $\theta = \cos^{-1}(x/c),$8 versus an experimental value of $\theta = \cos^{-1}(x/c),$9, corresponding to $c_l(y)$00 error; posterior conditioning further reduced $c_l(y)$01 to $c_l(y)$02 (Lee et al., 15 Aug 2025).

Across these test cases, the paper states that the error in $c_l(y)$03 did not exceed $c_l(y)$04 and that the model effectively captures three-dimensional effects such as those induced by wing tip vortices (Lee et al., 15 Aug 2025). It also reports a comparison against RANS using Spalart–Allmaras with 1.1M points, stating that LWM better captured the magnitude and extent of tip-vortex distortions in the outboard trailing-edge region, whereas RANS underpredicted them (Lee et al., 15 Aug 2025).

Training uses exact GP inference, which is reported as feasible because of the modest data size, with optimization by Adam from an initial learning rate of $c_l(y)$05, halved every 1000 epochs, for approximately 3000 epochs; an SWA-like procedure restores the best weights from three runs (Lee et al., 15 Aug 2025). Inference precomputes $c_l(y)$06 and is dominated by cross-covariance evaluation, reported as $c_l(y)$07 s on a single NVIDIA A100 GPU for approximately 25k surface points and approximately $c_l(y)$08 s on a Xeon E5-2660 CPU (Lee et al., 15 Aug 2025).

6. Broader LWM landscape, related datasets, and limitations

The 2025 LWM paper defines a specific probabilistic framework for finite-wing pressure and lift prediction, but later aerodynamic work uses the term more broadly to describe data-driven wing surrogates and generative systems (Lee et al., 15 Aug 2025). This suggests a widening usage of "Large Wing Model" from an uncertainty-aware predictor toward a larger ecosystem of aerodynamic representation learning, inverse design, and multi-fidelity modeling.

"OptiWing3D" (Diniz et al., 14 Dec 2025) describes a dataset explicitly positioned as enabling a Large Wing Model. It provides 1552 CFD evaluations yielding 776 successful 3D wing optimizations, initialized from distinct extruded airfoil cross-sections and paired in large part with 2D counterparts optimized under identical conditions, thereby forming a multi-fidelity dataset (Diniz et al., 14 Dec 2025). The associated baseline is a constraint-aware conditional latent diffusion model that predicts optimized wings from flow conditions, with a reported test-set shape MSE of $c_l(y)$09, normalized Vendi score of $c_l(y)$10, and volume constraint satisfaction of $c_l(y)$11 on $c_l(y)$12 test wings (Diniz et al., 14 Dec 2025). In that setting, LWM is framed not as a GP-based pressure predictor but as a possible learned model for optimized wing geometry conditioned on flow and constraints.

"SuperWing" (Yang et al., 16 Dec 2025) provides a different pathway. It is an open dataset of 4,239 parameterized wing geometries and 28,856 RANS flow-field solutions, with prepared surface meshes and labels suitable for transformer-based training (Yang et al., 16 Dec 2025). In the benchmark reported there, a Vision Transformer predicts surface fields on a common $c_l(y)$13 reference mesh and achieves approximately $c_l(y)$14 normalized MAE for $c_l(y)$15, $c_l(y)$16 for $c_l(y)$17, $c_l(y)$18 for $c_l(y)$19, and an integrated drag error of $c_l(y)$20, or 2.48 drag counts (Yang et al., 16 Dec 2025). The same paper reports strong zero-shot generalization to DLR-F6 and NASA CRM without fine-tuning (Yang et al., 16 Dec 2025). Relative to (Lee et al., 15 Aug 2025), this reflects a shift from sparse experimental data and explicit GP uncertainty to large-scale mesh-based supervised learning over transonic swept wings.

The original LWM also states clear limitations (Lee et al., 15 Aug 2025). Data coverage is sparse and biased toward rectangular wings and low-speed regimes; high sweep, strong taper, twist, and spanwise-varying airfoil sections are under-represented (Lee et al., 15 Aug 2025). Strong three-dimensional separation, stall, and highly compressible or shock-dominated regimes are outside the primary scope, and tip geometry is only implicitly rounded rather than explicitly modeled (Lee et al., 15 Aug 2025). The model further assumes a uniform airfoil section along the span, and exact GP inference imposes memory limits that motivate stochastic-variational or sparse-GP extensions for larger datasets (Lee et al., 15 Aug 2025). A plausible implication is that the probabilistic architecture of (Lee et al., 15 Aug 2025) and the broader datasets of (Diniz et al., 14 Dec 2025) and (Yang et al., 16 Dec 2025) are complementary rather than redundant: one emphasizes data efficiency and calibrated uncertainty under strict experimental scarcity, while the others emphasize geometric diversity, multi-fidelity pairing, and large-scale supervised or generative training.