Aerodynamic surrogate models trained on high-fidelity CFD data reproduce numerical predictions of both scalar outputs and entire fields accurately, yet their predictive fidelity is limited by systematic discrepancies between CFD and experimental observations. We present an experimentally grounded correction framework that adapts a CFD-trained deep learning surrogate using wind-tunnel PSP measurements. A Geotransolver surrogate trained on 2,300 high-fidelity CFD simulations of the NASA CRM wing-body configuration, spanning geometric variation, Mach 0.70-0.85, and angles of attack 0 to 4 degrees, reproduces the CFD integrated aerodynamic forces and pitching moment to R2 > 0.99 but does not match the experimental data. To incorporate experimental information without retraining the surrogate, a correction network is trained on spatially registered PSP measurements at two freestream Mach numbers (0.70 and 0.85) across the same angle-of-attack range, learning the discrepancy between the surrogate-predicted and experimentally measured surface-pressure distributions. At Mach 0.85 the correction substantially improves agreement with PSP, particularly at the wing suction peak, shock location, and subsequent pressure recovery, reducing both the magnitude of the prediction error and the fraction of wetted surface on which it exceeds 0.05 in Cp, and it does so from a limited experimental dataset without modifying the pretrained surrogate parameters. On held-out angles of attack the grounded surrogate agrees with measurement to within 2.3-2.7% of the measured Cp range, and outperforms direct interpolation between the measured conditions at every state tested. Experimental measurements can therefore ground a large-scale simulation-trained surrogate by learning systematic CFD-to-experiment discrepancies while preserving its generalization capability and computational efficiency.
Figures & tables
Figure 1: (a) Overview of the proposed simulation-to-experiment grounding framework. (b) Baseline architecture: training the surrogate on high-fidelity CFD datasets. (c) Correction framework: fine-tuning the surrogate using experimental data to learn the CFD-to-experiment discrepancy.
Figure 2: Lift, drag and pitching moments: baseline geotransolver surrogate model performance across the Mach 0.70 to 0.85 and AoA 0 ∘ to 4 ∘ flight envelope.
Figure 3: (a) Spanwise Cp distributions at M=0.85 comparing CFD, PSP, and corrected predictions at AoA 1.5 ∘ (a–c) and 3.0 ∘ (d–f) from near-root to near-tip. (b) Surface Cp fields from PSP, uncorrected, and corrected predictions.
M
AoA
R2
MAE
RMSE
Norm. err. (%)
Cp range
0.70
1.5 ∘
0.940
0.059
0.090
2.4
2.44
0.70
3.0 ∘
0.966
0.065
0.100
2.3
2.82
0.85
1.5 ∘
0.922
0.069
0.110
2.5
2.75
0.85
3.0 ∘
0.952
0.070
0.110
2.7
2.64
Table 1: Per-condition agreement between the grounded surrogate and PSP at held-out states. Normalized error is MAE divided by the measured Cp range.
Interpolation baseline
Grounded
ΔR2 from
Condition
raw
registered
surrogate
registration
correction
M=0.70 , AoA = 1.5 ∘
0.743
0.849
0.940
+0.106
+0.091
M=0.70 , AoA = 3.0 ∘
0.710
0.874
0.966
+0.164
+0.092
M=0.85 , AoA = 1.5 ∘
0.722
0.828
0.922
+0.106
+0.094
M=0.85 , AoA = 3.0 ∘
0.655
0.756
0.952
+0.101
+0.196
Table 2: Surface Cp agreement with PSP at held-out conditions. Interpolation uses raw, registered PSP fields, while the grounded surrogate combines the frozen backbone with the correction head.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Variable
Meaning
Range
AR
Aspect ratio
7.5 – 11
Λc/4
Quarter-chord sweep ( ∘ )
25 – 37.5
fcr
Root-chord extension factor
1.0 – 1.4
Df
Fuselage diameter (m)
6.096 – 6.553
τr
Root twist ( ∘ )
3 – 9
Δτk
Kink twist increment ( ∘ )
−7 to −3
Appendix
Table 3: Design of experiments for the SHIFT-Wing dataset. The seven geometry variables are sampled by Latin hypercube; angle of attack is swept and sideslip is fixed.
Figure 4: Coordinate registration pipeline. The delivered PSP field is indexed by structured grid position, so chordwise and spanwise coordinates are first reconstructed from the grid indices (Stage 1); the resulting measurement cloud is transferred onto the CFD surface nodes by inverse-distance weighted interpolation (Stage 2); and a Gaussian process is fitted over the surface to suppress measurement noise and fill nodes left without a valid paint return (Stage 3). The output is a registered Cpexp field carrying one value per CFD mesh cell, which is the target used for fitting and evaluating the correction head. Cells with no valid PSP return are masked and excluded from both.
Figure 5: Surface Cp parity plots: predicted versus experimental ground truth Cp across Mach 0.70 and 0.85 at AoA = 1.5 ∘ and 3.0 ∘ .
Figure 6: Spanwise Cp distribution: comparison of baseline CFD, experimental PSP measurements, and calibrated surrogate model predictions at Mach 0.70 across spanwise sections ( η=0.15 near root, η=0.50 mid-span, and η=0.85 near tip) for AoA = 1.5 ∘ (a–c) and AoA = 3.0 ∘ (d–f).
Figure 7: Full-surface Cp contours and error maps at Mach 0.70: comparison of experimental ground truth, Geotransolver prediction, and spatial error field. (a) AoA = 1.5 ∘ ( R2=0.940 , MAE =0.059 ). (b) AoA = 3.0 ∘ ( R2=0.966 , MAE =0.065 ).
Machine-learning surrogate models offer a promising alternative to high-fidelity Computational Fluid Dynamics (CFD) simulations for aerodynamic analysis and design. However, constructing accurate surrogates for realistic aircraft configurations remain challenging due to complex geometries, multiple flow regimes, and limited training data. This work presents the methodology that achieved first place in the ONERA CRM Wall Distribution Regression Challenge, which focuses on predicting pressure and skin-friction coefficient distributions over the NASA Common Research Model wing-body-pylon-nacelle configuration under different operating conditions. The proposed approach formulates the problem as a conditional neural field mapping spatial coordinates, surface normals, and operating conditions to aerodynamic wall quantities. Fourier feature encoding, a relative squared error objective aligned with the challenge metric, ensemble learning, and k-fold cross-validation are progressively introduced to improve prediction accuracy and exploit the limited training data. Beyond presenting the final methodology, the paper documents the successive model design choices that led to the winning solution through a comprehensive ablation study and discusses several alternative approaches that were investigated but ultimately discarded. On the hidden competition test set, the proposed methodology achieves an overall score of 8.81, outperforming the strongest organizer-provided baseline, which achieved a score of 8.64, while requiring approximately three orders of magnitude fewer trainable parameters. These results illustrate that carefully designed coordinate-based neural fields constitute an efficient and robust framework for aerodynamic surrogate modeling on complex geometries under limited-data conditions.
Accurate and efficient surrogate models for aerodynamic surface pressure fields are essential for accelerating aircraft design and analysis, yet deterministic regressors trained with pointwise losses often smooth sharp nonlinear features. This work presents a conditional denoising diffusion probabilistic model for predicting surface pressure distributions on the NASA Common Research Model wing under varying conditions of Mach number, angle of attack, and four control surface deflections. The framework operates on unstructured surface data through a principal component representation used as a non-truncated, reversible linear reparameterization of the pressure field, enabling a fully connected architecture. A signal-aware training objective is derived by propagating a reconstruction loss through the diffusion process, yielding a timestep-dependent weighting that improves fidelity in regions with strong pressure gradients. The stochastic sampling process is analyzed through repeated conditional generations, and two diagnostic metrics are introduced, the Local Reliability Index and Global Reliability Index, to relate sampling-induced spread to reconstruction error. Relative to the considered deterministic baselines, the proposed formulation reduces mean absolute error and improves the reconstruction of suction peaks, shock structures, and control surface discontinuities. The sampling-induced spread exhibits strong correspondence with surrogate error, supporting its interpretation as a qualitative reliability indicator rather than calibrated uncertainty quantification.
Víctor Francés-Belda, Carlos Sanmiguel Vila, Rodrigo Castellanos
Theoretical and Computational Aerodynamics Group Flight Physics Department. Subdirectorate General for Aeronautical Systems Spanish National Institute for Aerospace Technology (INTA) · Department of Aerospace Engineering Universidad Carlos III de Madrid Madrid, Spain · Aerial Platforms Department Subdirectorate General for Aeronautical Systems Spanish National Institute for Aerospace Technology (INTA)
Computational Fluid Dynamics (CFD) is central to race-car aerodynamic development, yet its cost -- tens of thousands of core-hours per high-fidelity evaluation -- severely limits the design space exploration feasible within realistic budgets. AI-based surrogate models promise to alleviate this bottleneck, but progress has been constrained by the limited complexity of public datasets, which are dominated by smoothed passenger-car shapes that fail to exercise surrogates on the thin, complex, highly loaded components governing motorsport performance. This work presents three primary contributions. First, we introduce a high-fidelity RANS dataset built on a parametric LMP2-class CAD model and spanning six operating conditions (map points) covering straight-line and cornering regimes, generated and validated by aerodynamics experts at Dallara to preserve features relevant to industrial motorsport. Second, we present the Gauge-Invariant Spectral Transformer (GIST), a graph-based neural operator whose spectral embeddings encode mesh connectivity to enhance predictions on tightly packed, complex geometries. GIST guarantees discretization invariance and scales linearly with mesh size, achieving state-of-the-art accuracy on both public benchmarks and the proposed race-car dataset. Third, we demonstrate that GIST achieves a level of predictive accuracy suitable for early-stage aerodynamic design, providing a first validation of the concept of interactive design-space exploration -- where engineers query a surrogate in place of the CFD solver -- within industrial motorsport workflows.
Nicholas Thumiger, Andrea Bartezzaghi, Mattia Rigotti +5