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MIFE-ONet: a multiscale information fusion feature equalization operator network for supercritical airfoil surface flow field prediction
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DOI：10.1007/s00366-026-02376-4.png)
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Abstract
En 中文
Accurate prediction of transonic surface flow fields over supercritical airfoils is essential for aerodynamic analysis and shape optimization. However, under transonic conditions, these surface flow fields exhibit both large scale smooth variations and shock-induced localized high-gradient structures. Existing deep learning models are prone to spectral bias when learning such multiscale features, leading to preferential convergence in smooth regions and insufficient fitting in localized high-gradient regions. To address this issue, we propose a Multiscale Information Fusion Feature Equalization Operator Network (MIFE-ONet), for surface flow field prediction over supercritical airfoils. In contrast to conventional multi-branch neural operators that mainly fuse branch features at the final stage, MIFE-ONet introduces layer-wise information fusion to progressively couple geometry, angle of attack, and surface-position features. This strengthens the interaction among heterogeneous inputs and improves the prediction accuracy of surface flow fields. A neural tangent kernel (NTK) analysis further shows that unequal residual convergence rates across feature directions contribute to the imbalanced learning of multiscale flow structures. Accordingly, MIFE-ONet employs multiple trunk branches with different scale transformations applied to the same surface coordinates, allowing the model to learn flow field features at different effective spatial scales and improving the prediction balance between smooth regions and localized high-gradient structures. Experimental results show that MIFE-ONet achieves the best performance across four error metrics, with a mean relative error (MRE) of 6.40%, representing a 20.5% reduction compared with the best baseline model. Further analysis of local shock characteristics demonstrates that the proposed model captures shock location, pressure-jump magnitude, and localized high-gradient structures more accurately, verifying its reliability for transonic surface flow field prediction.
Keywords:
Supercritical airfoil
Neural operator
Information fusion
Multiscale feature equalization learning
Multiscale information fusion feature equalization operator
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