LGFNet: Local-Global Fusion Network with Fidelity Gap Delta Learning for Multi-Source Aerodynamics

Qinye Zhu; Yu Xiang; Jun Zhang; Wenyong Wang

cs.LGMar 31, 2026

LGFNet: Local-Global Fusion Network with Fidelity Gap Delta Learning for Multi-Source Aerodynamics

Authors: Qinye Zhu, Yu Xiang, Jun Zhang, Wenyong Wang

Organizations: School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China

Abstract

The precise fusion of computational fluid dynamic (CFD) data, wind tunnel tests data, and flight tests data in aerodynamic area is essential for obtaining comprehensive knowledge of both localized flow structures and global aerodynamic trends across the entire flight envelope. However, existing methodologies often struggle to balance high-resolution local fidelity with wide-range global dependency, leading to either a loss of sharp discontinuities or an inability to capture long-range topological correlations. We propose Local-Global Fusion Network (LGFNet) for multi-scale feature decomposition to extract this dual-natured aerodynamic knowledge. To this end, LGFNet combines a spatial perception layer that integrates a sliding window mechanism with a relational reasoning layer based on self-attention, simultaneously reinforcing the continuity of fine-grained local features (e.g., shock waves) and capturing long-range flow information. Furthermore, the fidelity gap delta learning (FGDL) strategy is proposed to treat CFD data as a "low-frequency carrier" to explicitly approximate nonlinear discrepancies. This approach prevents unphysical smoothing while inheriting the foundational physical trends from the simulation baseline. Experiments demonstrate that LGFNet achieves state-of-the-art (SOTA) performance in both accuracy and uncertainty reduction across diverse aerodynamic scenarios.

Figures & tables

Symbol	Description
$\mathbf{x}$	Input aerodynamic state vector
$\mathbf{y}$	Output aerodynamic response vector
$\mathbf{d}=[\mathbf{x},\mathbf{y}]$	Unified aerodynamic data vector
$N_{L},N_{H}$	The quantity of samples in low-fidelity (CFD) and high-fidelity datasets
$\mathcal{D}_{L},\mathcal{D}_{H}$	Original low-fidelity and high-fidelity datasets
$\mathcal{T}_{L},\mathcal{T}_{H}$	Aligned datasets generated via sliding window transformation

Table 1: Relevant Definitions and Notations

Figure 1: The architecture of Local-Global Fusion Network (LGFNet) model. (a) data alignment module, (b) LGFNet module.

Figure 2: Sliding Window (SW) mechanism.

Case	Mach ( $Ma$ )	Reynolds ( $Re$ )	AoA ( $\alpha$ )
Case 1	0.729	$6.5\times 10^{6}$	$2.31^{\circ}$
Case 2	0.730	$6.5\times 10^{6}$	$3.19^{\circ}$
Case 3	0.600	$6.3\times 10^{6}$	$2.57^{\circ}$

Table 2: The inflow conditions for the RAE2822 airfoil test cases.

Panel of Figure 3 — Figure 3: Comparison between CFD simulations and Wind data.

Workflow Phase	Scenario 1: RAE2822 Airfoil	Scenario 2: CARDC Aircraft
Primary Challenge	Scarcity of discrete operating cases	Continuity of high-dimensional trajectories
Data Partitioning	Case-wise rotating split via “Leave-Half-Out” strategy (training : testing = 2.5 : 0.5)	Block-wise cyclical split via Mach number jumps (training : testing = 4 : 1)
Training Strategy	Hyperparameter tuning via 5-fold cross-validation, followed by full-set retraining	Data augmentation via sliding window mechanism, followed by standard network training
Evaluation Metric	Quantitative assessment on the sealed test set using RMSE, MAE, and $R^{2}$
Final Inference	Comprehensive database generation via full-sequence inference

Table 3: Comparison of training and inference workflows.

Case	Model	RMSE $\downarrow$	MAE $\downarrow$	$R^{2}$ $\uparrow$	Time(s)	Uncertainty $\downarrow$
Case 1	WIND (Exp.)	-	-	-	-	0.7887
	HK	0.1503	0.09769	0.9422	6.08	0.2852
	DNN	0.1704	0.1165	0.9290	242.60	0.2341
	MSFM	0.1682	0.1092	0.9308	118.99	0.2648
	XGBoost	0.3256	0.2216	0.7410	5.58	0.2956
	ArGEnT	0.0681	0.0552	0.9887	17.02	0.1695

Table 4: Quantitative comparison of four fusion models on RAE2822 dataset.

Panel of Figure 4 — Figure 4: Comparison results across three cases. The top row (a-c) shows the pressure coefficient ( $C_{p}$ ) fusion curves on the test set of the target case, while the bottom row (d-f) displays the fusion curves on the full dataset of the target case.

Case	Model	RMSE $\downarrow$	MAE $\downarrow$	$R^{2}$ $\uparrow$	Time(s)	Uncertainty $\downarrow$
$C_{x}$	FLI (Exp.)	-	-	-	-	0.3394
	DNN	0.0037	0.0023	0.9923	188.84	0.1948
	MSFM	0.0040	0.0025	0.9909	668.26	0.2078
	XGBoost	0.0043	0.0028	0.9892	2.43	0.1943
	ArGEnT	0.0042	0.0032	0.9850	58.22	0.2453
	LGFNet (Ours)	0.0042	0.0027	0.9848	243.88	0.1953

Table 5: Quantitative comparison of four fusion models on CARDC aircraft dataset.

Panel of Figure 5 — Figure 5: Comparison results of different aerodynamic coefficients.

Panel of Figure 6 — Figure 6: Surface comparison of FLI,CFD and LGFNet with respect to aerodynamic coefficients.

Model Variant	Case	RMSE	MAE	$R^{2}$
LGFNet (w/o SW & Att)	Case 1	0.0892	0.0758	0.9805
LGFNet (w/o SW)	Case 1	0.0821	0.0559	0.9835
LGFNet (w/o Att)	Case 1	0.0791	0.0551	0.9847
LGFNet (Full)	Case 1	0.0591	0.0394	0.9915
LGFNet (w/o SW & Att)	Case 2	0.0846	0.0763	0.9835
LGFNet (w/o SW)	Case 2	0.0717	0.0512	0.9882

Table 6: Ablation study results on RAE2822 airfoil dataset.

Model Variant	Coeff.	RMSE	MAE	$R^{2}$
LGFNet (w/o SW & Att)	$C_{x}$	0.0075	0.0053	0.9752
LGFNet (w/o SW)	$C_{x}$	0.0058	0.0042	0.9789
LGFNet (w/o Att)	$C_{x}$	0.0056	0.0039	0.9812
LGFNet (Full)	$C_{x}$	0.0042	0.0031	0.9848
LGFNet (w/o SW & Att)	$C_{y}$	0.0094	0.0076	0.9654
LGFNet (w/o SW)	$C_{y}$	0.0082	0.0061	0.9712

Table 7: Ablation study results on CARDC aircraft dataset.

Multi-Scale Feature Fusion

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FSAN: Flow State Attention Network for Aerodynamic Prediction

Wenxuan Jin, Jianguo Yao, Haibing Guan, Xijun Li

Shanghai Key Laboratory of Scalable Computing and Systems · School of Computer Science, Shanghai Jiao Tong University

Neural Surrogate Modeling PDE Surrogate Modeling Computational Fluid Dynamics

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Accurate aerodynamic prediction is critical for designing fuel-efficient and safe transportation systems such as aircraft and automobiles, yet traditional computational fluid dynamics (CFD) simulations remain computationally expensive and expertise-intensive, severely limiting their use in iterative design and real-time analysis. Existing deep learning surrogates suffer from two major limitations: (i) they are evaluated on datasets with narrow flow-condition ranges, leaving their performance under complex flow conditions undemonstrated; (ii) they treat global flow conditions as a single vector injected uniformly across all surface points, ignoring that different geometric regions experience distinct local flow phenomena, which degrades prediction accuracy under complex flow conditions. To address these limitations, we propose the Flow State Attention Network (FSAN). FSAN separately encodes point cloud and flow conditions, then partitions the geometry into multiple flow states via learnable soft assignments, and uses flow features to update these state representations, which in turn influence point cloud features through state changes. This enables fine-grained, state-specific interaction between geometry and flow information. Extensive experiments on two well-recognized aerodynamic benchmarks demonstrate that FSAN achieves the highest accuracy among the methods compared in this work at a higher computational cost. On Emmi-Wing, FSAN reduces the Relative L2 (REL-L2) error by over 20% compared to the strongest baseline (Transolver), and on DrivAerNet++, it achieves a 10% reduction compared to the strongest baseline (AdaField). These results establish FSAN as a promising neural surrogate on public benchmarks with diverse flow conditions and geometries.

Abstract

Multi-Scale Feature Fusion

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