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A Data Fusion Framework for Grounding Aerospace Surrogate Model via Experimental Wind-Tunnel Observations

Nitin Nagesh Kulkarni, Dheeraj Vemula, Yin Yu, Peter Lyu, Juan J. Alonso

arXiv:2609.04267v1cs.LG

TL;DR

CFD-trained aerodynamic surrogates inherit systematic discrepancies between simulation and experiment, while experimental measurements are limited. This paper trains a correction head on registered PSP measurements without retraining the pretrained surrogate; held-out predictions achieve low normalized error and outperform direct interpolation.

  • Problem

    CFD-trained surrogates inherit simulation discrepancies, while experimental measurements are expensive and limited across flight conditions.

    Source: §1 · p. 2

  • Method

    A lightweight correction head learns CFD-to-experiment pressure discrepancies from spatially registered PSP measurements while the pretrained Geotransolver remains fixed.

    Source: §2 · p. 2, §2.3 · p. 3

  • Results

    2.3–2.7% errors relative to the measured Cp range at held-out conditions, with corrected predictions outperforming direct interpolation at every tested state.

    Source: §4 · p. 5

  • Takeaways & Limitations

    Limited experimental data can ground a simulation-trained surrogate while retaining its broad aerodynamic representation and computational efficiency.

    Source: §4 · p. 5

    Correction is evaluated at only two Mach numbers, so behavior outside 0.70 ≤ M ≤ 0.85 is untested.

    Source: §A.6 · p. 11

Abstract

from arXiv · show

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.

1 Introduction

Simulation-trained aerodynamic surrogates inherit the fidelity limits of CFD, while experiments provide physical observations but are too limited to train deep surrogates alone. This motivates fusing broad simulation coverage with experimental data to correct systematic discrepancies in a pretrained surrogate.

1 Introduction

  • CFD modeling and discretization errors can propagate into surrogate predictions, while limited experimental measurements cannot alone support deep-surrogate training.PSP provides dense surface-pressure fields and captures effects that can be difficult to model accurately.Source: §1 · p. 2
  • Existing data-fusion approaches mainly combine fidelity levels through statistical or explicit correction models rather than modifying a pretrained surrogate’s learned representation.The paper frames this as a gap in how simulation-trained surrogate representations are grounded by experimental data.Source: §1 · p. 2
  • The proposed framework uses limited experimental observations to correct systematic discrepancies in a pretrained simulation-based surrogate while preserving its simulation coverage and computational efficiency.The authors describe this as a closed-loop connection between simulation, surrogate modeling, and experiment.Source: §1 · p. 2

2 Method

The method combines a surrogate pretrained on broad CFD data with a lightweight correction head trained on spatially registered wind-tunnel PSP measurements. The pretrained Geotransolver stays fixed while the head learns CFD-to-experiment discrepancies.

2 Method

  • A frozen CFD-pretrained surrogate and an experimental correction head form the proposed simulation-to-experiment grounding workflow.Figure 1 contrasts the CFD-trained baseline architecture with the correction framework.Source: §2 · p. 2, Figure 1 · p. 3

2.1 Datasets

  • The dataset contains 2,300 high-fidelity NASA CRM simulations across Mach 0.70–0.85 and angles of attack 0°–4°, plus PSP measurements at two Mach numbers.At each Mach number, PSP covers nine angles of attack; 1.5° and 3.0° are withheld for testing, and pressures are converted to Cp for comparison and correction training.Source: §2.1 · pp. 2–3

2.2 Baseline Surrogate

  • The Geotransolver predicts surface-pressure fields from wing geometry and flow conditions, using geometry-aware features and GALE attention blocks to represent spatial interactions.After CFD training, its parameters are frozen and its learned latent representation serves as the prior for experimental correction.Source: §2.2 · p. 3

2.3 Experimental Correction

  • A lightweight MLP correction head receives the frozen Geotransolver’s per-cell latent features and normalized flow conditions, then predicts pressure from registered PSP measurements.Only the correction head is trainable, so experimental data teach it systematic discrepancies without retraining the pretrained backbone.Source: §2.3 · p. 3

3 Results

The grounded surrogate improves held-out agreement with PSP over direct interpolation, while the uncorrected surrogate reproduces CFD loads but retains localized pressure discrepancies against experiment. The correction shifts predictions toward PSP near suction peaks, shocks, and pressure recovery.

3 Results

  • R² > 0.99 for lift, drag, and pitching moment across Mach 0.70–0.85 and angles of attack 0°–4°, but this CFD agreement does not establish experimental validation.At M = 0.85, PSP comparisons reveal localized discrepancies near suction peaks and downstream pressure recovery, with shock-location differences increasing toward mid- and outboard-span regions.Source: §3 · p. 4, Figure 2 · p. 4

3.1 Quantitative agreement and interpolation baseline

  • 2.3–2.7% normalized error across the four held-out conditions, with R² = 0.922–0.966 against registered PSP fields.Normalized error is MAE divided by the measured Cp range; Table 1 reports per-condition agreement.Source: §3.1 · p. 4, Table 1 · p. 5
  • 0.09–0.20 R² improvement over the registered interpolation baseline, with the grounded surrogate outperforming interpolation at every held-out condition.At M = 0.85 and AoA = 3.0°, interpolation gives R² = 0.756 while the grounded surrogate gives R² = 0.952, a margin of 0.196.Source: Table 2 · p. 5, §3.1 · p. 5
  • The correction captures discrepancies absent from rigid-geometry CFD training, particularly in shock location, suction-peak magnitude, and pressure recovery, without isolating their individual sources.Possible contributors include aeroelastic deformation, transition behavior, turbulence modeling, facility conditions, and model-form uncertainties.Source: §3.1 · p. 5

4 Conclusion

The study grounds a CFD-trained Geotransolver with a correction head trained on registered PSP, reducing held-out pressure errors and outperforming direct interpolation. The authors conclude that limited experimental data can ground the simulation-trained surrogate while retaining its broad aerodynamic representation and computational efficiency.

4 Conclusion

  • At held-out conditions, corrected predictions have errors of 2.3–2.7% of the measured Cp range and outperform direct interpolation at every tested state.The backbone is frozen while a compact correction head is trained on registered PSP measurements.Source: §4 · p. 5

A.1 Training dataset and hyperparameters

The SHIFT-Wing training set varies NASA CRM geometry alongside flight conditions, with angle of attack swept and sideslip fixed. The section also specifies the CFD and correction-head training setup.

A.1 Training dataset and hyperparameters

  • The SHIFT-Wing training dataset comprises 2,262 high-fidelity RANS solutions of the NASA CRM wing-body configuration, with 1,130 at Mach 0.70 and 1,132 at Mach 0.85, drawn from 2,330 generated cases.The seven geometry variables are sampled by Latin hypercube; angle of attack is swept and sideslip is held at zero.Source: §A.1 · p. 8, Table 3 · p. 8
  • The Geotransolver baseline is trained for 500 epochs on an area-weighted normalized surface-pressure loss, using an initial learning rate of 10^-4 and eight H100 GPUs.The dataset is split 90/10 for training and validation.Source: §A.1 · p. 8
  • The correction head is a 140,289-parameter four-layer MLP trained for 200 epochs on pooled per-cell points, while the backbone remains frozen.Its 386 inputs combine a 384-dimensional latent with Mach number and angle of attack; the 18 experimental conditions are divided into training, validation, and held-out test sets.Source: §A.1 · p. 8

A.2 Formulation of the correction head

The correction head uses the frozen CFD-trained backbone’s per-cell latent representation and flow conditions to predict measured pressure. It is fitted to registered PSP data without a CFD anchoring term and is not constrained to an additive correction.

A.2 Formulation of the correction head

  • For each surface cell, the frozen backbone maps geometry and flow condition to a latent representation, and its decoder reproduces the CFD field.The correction head receives the latent concatenated with normalized Mach number and angle of attack, then predicts experimentally observed pressure.Source: §A.2 · p. 8
  • The correction head is fitted by minimizing mean squared error against registered measurements over valid wing-surface cells.The loss is unweighted, acts on surface Cp alone, and uses no CFD anchoring term.Source: §A.2 · p. 9
  • Unlike prescribed additive or multiplicative corrections, the head learns an unconstrained nonlinear mapping from the frozen latent to measured pressure.Additive and multiplicative corrections remain representable as special cases; only the correction head’s 140,289 parameters are fitted to experiment.Source: §A.2 · p. 9

A.3 PSP registration procedure

PSP measurements and CFD solutions occupy different domains, so registration maps the measured pressure field onto the CFD mesh for pointwise fitting and evaluation. The procedure reconstructs coordinates, interpolates measurements, and applies a Gaussian process, while masking invalid-return cells.

A.3 PSP registration procedure

  • Registration first reconstructs physical chordwise and spanwise coordinates from PSP grid indices, then transfers measurements to CFD surface nodes by inverse-distance weighted interpolation.An unregistered interpolation baseline loses 0.10–0.16 in R2 relative to the registered-field baseline.Source: §A.3 · p. 9
  • A Gaussian process smooths measurement noise and fills nodes without valid paint return, producing a registered pressure field with one value per CFD mesh cell.The registered field is the correction head’s fitting and evaluation target.Source: §A.3 · p. 9, Figure 4 · p. 9
  • Cells without valid PSP returns are masked and excluded from both fitting and evaluation because optical access leaves surface gaps.The gaps occur at edges and component junctions.Source: §A.3 · p. 9, Figure 4 · p. 9
  • Registration carries error because the as-built model and its aeroelastic deflection do not exactly match the nominal CAD surface used for the CFD mesh.The raw-versus-registered comparison in Table 2 bounds how much reported agreement depends on registration.Source: §A.3 · p. 10

A.4 Aeroelastic wing deflection

The wind-tunnel model deforms under aerodynamic load, so its measured pressure field is not on the nominal rigid geometry used in CFD. The resulting washout is associated with reduced suction and lift and a forward-shifted or absent shock.

A.4 Aeroelastic wing deflection

  • At the M = 0.85 cruise design point, published NASA CRM measurements report approximately 25 mm of tip bending and −0.5° of tip twist.The flexible wind-tunnel model bends upward and twists nose-down relative to its unloaded shape; deformation scales approximately with q∞CL.Source: §A.4 · p. 10
  • Washout unloads the mid-span and tip, bringing upper- and lower-surface Cp distributions closer together and reducing suction-peak magnitude and lift.It also shifts the shock forward toward the leading edge or removes it; some CFD-to-PSP discrepancy therefore reflects geometric mismatch rather than turbulence or transition modeling deficiencies.Source: §A.4 · p. 10

A.5 Additional results

Across the measured conditions, the calibrated surrogate agrees with PSP in parity metrics and captures spanwise and full-surface pressure patterns at Mach 0.70. The reported accuracy is within the measured envelope.

A.5 Additional results

  • Across four conditions, area-weighted R2 = 0.938–0.953, MAE = 0.046–0.061 and RMSE = 0.063–0.089 in Cp.Figure 5 compares predicted and experimental Cp at Mach 0.70 and 0.85 and AoA 1.5° and 3.0°; the reported consistency supports accuracy within, not beyond, the measured envelope.Source: §A.5 · p. 10, Figure 5 · p. 10
  • At Mach 0.70, full-surface comparisons show spatial agreement, with residual differences concentrated near the leading edge and wing tip.Figure 7 reports R2 = 0.940 and MAE = 0.059 at AoA 1.5°, and R2 = 0.966 and MAE = 0.065 at AoA 3.0°.Source: §A.5 · p. 10, Figure 7 · p. 11
  • At Mach 0.70, calibrated spanwise Cp distributions align with PSP at the root, mid-span and tip for AoA 1.5° and 3.0°.The correction addresses localized suction-peak and trailing-edge pressure-recovery deviations in the baseline CFD distributions.Source: §A.5 · p. 10, Figure 6 · p. 11

A.6 Limitations

The reported evidence is limited to two Mach numbers and one experimental configuration, and the correction does not distinguish individual sources of CFD-to-experiment discrepancy.

A.6 Limitations

  • Correction behavior outside 0.70 ≤ M ≤ 0.85 is untested; the reported held-out-angle accuracy does not establish extrapolation beyond that envelope.The correction is fitted and evaluated at only two Mach numbers.Source: §A.6 · p. 11
  • PSP data cover one configuration, leaving transfer of a correction learned on that geometry to other SHIFT-Wing family geometries unresolved.Source: §A.6 · p. 11
  • The empirical correction captures combined CFD-to-experiment discrepancies without identifying or separating their individual mechanisms.The aeroelastic contribution is offered as a physical interpretation rather than an identified term.Source: §A.6 · p. 11
  • Results are reported as ranges across four flow conditions, not as variance over training seeds.Source: §A.6 · p. 11
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