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<p>Obtaining high-fidelity aerodynamic database for modern aircraft remains challenging in terms of cost. To reduce the requirement of high-fidelity data on current aerodynamics, this research proposes a data fusion integrated neural network (LambdaNN). Distinct from previous research, this study condenses a novel correlation of multi-fidelity data, embedding it into the model structure and operator design to enhance the representation of data fusion frameworks. Instead of serial and sequential modeling in typical multi-fidelity neural networks (MFNN), LambdaNN separates features into common and private components through a shared-parallel structure. It reduces the influence of low-fidelity private features, thus improving the accuracy and robustness of fusion models under less data consistency. The resulting model is called LambdaNN, since its parallel fusion structure resembles a horizontally laid <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="158_2025_4013_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>. This model is compared with co-kriging and MFNN. Various examples are used for validation, including analytical examples with strong consistency and aerodynamics prediction with less consistency. The results show that LambdaNN performs well with strong data consistency. Furthermore, LambdaNN also exhibits reasonable accuracy when the data consistency is weak. In particular, for ONERA-M6 wing modeling, LambdaNN can lower the root mean square error (RMSE) by approximately 40% compared to co-kriging and, on average, achieve a 20% reduction in RMSE compared to MFNN. Additionally, LambdaNN is structurally flexible and easily extended to high-dimensional complex aerodynamic issues.</p>

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Multi-fidelity aerodynamic fusion modeling via shared-parallel neural network structure

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • Chenjia Ning,
  • Jiaqing Kou,
  • Kai Li,
  • Xu Wang,
  • Weiwei Zhang

摘要

Obtaining high-fidelity aerodynamic database for modern aircraft remains challenging in terms of cost. To reduce the requirement of high-fidelity data on current aerodynamics, this research proposes a data fusion integrated neural network (LambdaNN). Distinct from previous research, this study condenses a novel correlation of multi-fidelity data, embedding it into the model structure and operator design to enhance the representation of data fusion frameworks. Instead of serial and sequential modeling in typical multi-fidelity neural networks (MFNN), LambdaNN separates features into common and private components through a shared-parallel structure. It reduces the influence of low-fidelity private features, thus improving the accuracy and robustness of fusion models under less data consistency. The resulting model is called LambdaNN, since its parallel fusion structure resembles a horizontally laid \(\lambda\) λ . This model is compared with co-kriging and MFNN. Various examples are used for validation, including analytical examples with strong consistency and aerodynamics prediction with less consistency. The results show that LambdaNN performs well with strong data consistency. Furthermore, LambdaNN also exhibits reasonable accuracy when the data consistency is weak. In particular, for ONERA-M6 wing modeling, LambdaNN can lower the root mean square error (RMSE) by approximately 40% compared to co-kriging and, on average, achieve a 20% reduction in RMSE compared to MFNN. Additionally, LambdaNN is structurally flexible and easily extended to high-dimensional complex aerodynamic issues.