InBreast: Multi-Source Aerodynamic Data Fusion

• InBreast is a multi-source aerodynamic data fusion framework that quantifies the fidelity gap between CFD surrogates and high-fidelity experimental measurements.
• It employs a Local-Global Fusion Network with Fidelity Gap Delta Learning to model nonlinear discrepancies and preserve both local and global aerodynamic features.
• The approach achieves up to a 71% reduction in RMSE and an 80% decrease in uncertainty, ensuring accurate capture of shocks and global trends.

In multi-source aerodynamic data fusion, the fidelity gap quantifies the systematic discrepancy between predictions from low-fidelity computational models (such as Reynolds-averaged Navier–Stokes-based CFD surrogates) and high-fidelity experimental measurements (such as wind-tunnel or flight-test data). Closing this gap is critical for reliable multi-scale inference of both local flow features and global aerodynamic trends. The Local-Global Fusion Network (LGFNet) with Fidelity Gap Delta Learning (FGDL) provides a rigorous architecture and learning strategy to address these challenges by decomposing and learning the nonlinear discrepancies that separate physical simulation and experiment.

1. Formal Definition of the Fidelity Gap

Given an aerodynamic state vector $x \in \mathbb{R}^n$ (for example, comprising Mach number, angle of attack, and control deflections), denote the low-fidelity response (e.g., CFD prediction) as $y_L(x)$ and the high-fidelity “ground truth” (e.g., wind-tunnel or flight-test measurement) as $y_H(x)$. The fidelity gap is characterized by the residual

$y_H(x) = y_L(x) + R_\mathrm{gap}(x, y_L(x)),$

where $R_\mathrm{gap}(x, y_L(x))$ is the unknown systematic error between the two sources. Equivalently, the pointwise fidelity gap can be written as

$\Delta(x) \equiv y_H(x) - y_L(x).$

The task of multi-source aerodynamic fusion is reformulated as learning a model that, for each state $x$, predicts the nonlinear discrepancy $\Delta(x)$; the reconstructed high-fidelity prediction is then $\hat{y}(x) = y_L(x) + \hat{\Delta}(x)$, with $\hat{\Delta}(x)$ a learned approximation of $y_L(x)$0 (Zhu et al., 31 Mar 2026).

2. Fidelity Gap Delta Learning (FGDL) Formulation

The FGDL strategy treats the CFD surrogate as a "low-frequency carrier" and targets the modeling of the high-frequency, nonlinear residual. Specifically, the network is tasked not with fitting $y_L(x)$1 directly, but rather learning $y_L(x)$2, exploiting the decomposition:

• $y_L(x)$3 (the CFD baseline),
• $y_L(x)$4,
• The learning objective is minimizing the mean squared error:

$y_L(x)$5

where $y_L(x)$6 is produced by LGFNet given the input $y_L(x)$7.

At inference, output synthesis is performed as $y_L(x)$8, ensuring consistency with the original physical trend encoded in the CFD surrogate.

3. LGFNet Architecture: Local-Global Feature Fusion

LGFNet is constructed with explicit architectural priors to capture both localized discontinuities (e.g., shock waves) and long-range correlations across aerodynamic states:

• Spatial Perception Layer (SPL): Applies a sliding window over the batch-ordered data matrix $y_L(x)$9 to create overlapping local context blocks $y_H(x)$0. Each block passes through a hierarchy of 2D convolutional stages (with increasing channel dimension and max-pooling over the window length) to encode sharp spatial gradients and local discontinuities.
• Relational Reasoning Layer (RRL): After flattening the output of SPL, this stage applies multi-head self-attention, incorporating positional encodings, to enable the capture of long-range dependencies (e.g., interactions from leading to trailing edge on an airfoil). The output is added back (residual connection) to the local features, which acts as a learned low-pass filter on the residual, curbing interpolation artifacts without erasing physical sharpness.
• Feature Synthesis Layer (FSL): A symmetric upsampling decoder with skip connections recombines feature maps to reconstruct the residual $y_H(x)$1. Final output is generated via a $y_H(x)$2 convolution.

The entire architecture is optimized end-to-end with the FGDL loss, ensuring that only the modeled mismatch is learned, which mitigates risks of data-driven over-smoothing (Zhu et al., 31 Mar 2026).

4. Prevention of Unphysical Smoothing by FGDL

Traditional direct-fusion or purely data-driven models tend to oversmooth high-resolution signals, especially at discontinuities, due to network bias and lack of explicit physical anchoring. FGDL circumvents this by:

• Restricting the network's representational duty to only the high-frequency components (residuals) with respect to $y_H(x)$3, thus the broad physical trend (global flow structure) is inherited directly from the CFD baseline and cannot be erased by the network.
• The sliding-window design of SPL preserves sharp local features by focusing on overlapping local contexts.
• The self-attention RRL smooths the residual only in a learned, physically consistent way, avoiding the artificial global smoothing that plagues many regression frameworks.

In summary, LGFNet+FGDL achieves high expressivity for shocks and local phenomena while maintaining the global template imposed by the baseline CFD model, thereby avoiding unphysical artifacts.

5. Quantitative Performance and Fidelity Gap Closure

Extensive experiments on RAE2822 airfoil (distribution fusion) and the CARDC aircraft (coefficient fusion) demonstrate systematic closure of the fidelity gap:

Task / Case	RMSE (CFD→Exp)	RMSE (LGFNet)	RMSE Reduction	Uncertainty Reduction
RAE2822 (Case 1, Transonic)	0.1503	0.0591	61%	80%
RAE2822 (Case 2)	0.1887	0.0607	68%	80%
RAE2822 (Case 3, Subsonic)	0.2043	0.0597	71%	71%
CARDC $y_H(x)$4 (Lateral Force)	~0.0233 (MSFM)	0.0169	–	81%

Uncertainty is evaluated as the 95% confidence interval width in predictive distributions. The model achieves RMSE $y_H(x)$5 0.06—state-of-the-art among methods compared (best competitors $y_H(x)$6 0.07)—with uncertainty levels sharply below either pure experiment or deep neural network baselines (Zhu et al., 31 Mar 2026).

On aircraft force coefficients, similar gains are observed for $y_H(x)$7, $y_H(x)$8, and $y_H(x)$9, both in error magnitude and $y_H(x) = y_L(x) + R_\mathrm{gap}(x, y_L(x)),$0.

6. Theoretical and Practical Implications

The LGFNet+FGDL methodology evidences that precise decomposition and residual learning are critical for multi-source data fusion in aerodynamics. By closing up to 70% of the error and 80% of the uncertainty gap, it enables physically faithful inference of both sharp local and global aerodynamic responses. This approach is broadly applicable to other scientific problems where multi-fidelity fusion is needed and physical interpretability is essential.

7. Summary Table

Component	Role in Closing Fidelity Gap	Mechanism
Low-Fidelity Carrier	Preserves global CFD-predicted trends	Reference trajectory for residual learning
Residual Prediction	Models high-frequency, nonlinear mismatch	Deep network trained on $y_H(x) = y_L(x) + R_\mathrm{gap}(x, y_L(x)),$1
SPL (Sliding Window)	Encodes sharp local features (e.g., shocks)	Windowed convolutions keep spatial discontinuity
RRL (Self-Attention)	Captures global dependencies, filters noise	Multi-head attention on residual sequence
FSL (Decoder)	Reconstructs fused local-global predictions	Upsampling with skip connections

This structured approach sharply distinguishes between large-scale simulation bias and unresolved local nonlinearities, providing a scalable path to comprehensive, uncertainty-aware aerodynamic knowledge extraction (Zhu et al., 31 Mar 2026).