A Hybrid CNN-Cheby-KAN Framework for Efficient Prediction of Two-Dimensional Airfoil Pressure Distribution

TL;DR

The paper addresses efficient prediction of two-dimensional airfoil pressure distributions by introducing a hybrid CNN-Cheby-KAN framework that encodes airfoil geometry with a CNN into a 16-dimensional latent vector and predicts pressure fields with a Chebyshev-enhanced Kolmogorov-Arnold Network, using inputs that include spatial coordinates and flow conditions. It reports $MSE \approx 10^{-6}$ and $R^2 > 0.999$ across multiple airfoils and conditions, outperforming MLP baselines, with an optimal training dataset size around $3\times 10^5$ samples. The approach yields a high-accuracy, data-driven surrogate suitable for rapid aerodynamic predictions, though it exhibits localized errors in boundary-layer regions and flow separation scenarios due to the absence of embedded physics. This work advances surrogate modeling for CFD-like predictions and offers potential for accelerated aerodynamic design optimization, while pointing to future improvements through physics-informed constraints.

Abstract

The accurate prediction of airfoil pressure distribution is essential for aerodynamic performance evaluation, yet traditional methods such as computational fluid dynamics (CFD) and wind tunnel testing have certain bottlenecks. This paper proposes a hybrid deep learning model combining a Convolutional Neural Network (CNN) and a Chebyshev-enhanced Kolmogorov-Arnold Network (Cheby-KAN) for efficient and accurate prediction of the two-dimensional airfoil flow field. The CNN learns 1549 types of airfoils and encodes airfoil geometries into a compact 16-dimensional feature vector, while the Cheby-KAN models complex nonlinear mappings from flight conditions and spatial coordinates to pressure values. Experiments on multiple airfoils--including RAE2822, NACA0012, e387, and mh38--under various Reynolds numbers and angles of attack demonstrate that the proposed method achieves a mean squared error (MSE) on the order of $10^{-6}$ and a coefficient of determination ($R^2$) exceeding 0.999. The model significantly outperforms traditional Multilayer Perceptrons (MLPs) in accuracy and generalizability, with acceptable computational overhead. These results indicate that the hybrid CNN-Cheby-KAN framework offers a promising data-driven approach for rapid aerodynamic prediction.

Figures (18)

• Figure 1: Convolution operations under multiple convolution kernels
• Figure 2: Schematic diagram of maximum pooling principle
• Figure 3: The complete structure of convolutional neural networks
• Figure 4: Schematic diagram of Kolmogorov Arnold networks structure
• Figure 5: Comparison of MSE after network training with different structures