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<p>Understanding the nonlinear evolution of complex fluid dynamics systems under parameter variations has long been a significant challenge in both engineering and scientific fields. This paper addresses the problem of parameterized flow modeling for pitching airfoils under low Reynolds number and high angle-of-attack conditions. It combines time-delay embedding methods to tackle partial observability issues and utilizes complex network theory to transform data structures, proposing an innovative data-driven reduced-order modeling approach based on complex networks. The dimensionality reduction process employs the Time-Delay Laplacian Eigenmaps with K-Nearest Neighbors (TDLE-KNN) algorithm. This method effectively maps flow field data to a low-dimensional space, balancing high interpretability with low reconstruction error. Phase analysis reveals the latent dynamic characteristics of the system, where the evolution of phase angles reflects the system's inherent dynamics, and the variation in radial distances quantitatively describes the influence mechanism of system parameters. Furthermore, we have developed the Shared Dynamics Information Complex Network Modeling (SDCNM) framework, based on the assumption that multi-parameter systems share common latent dynamic characteristics. These shared features are represented in SDCNM through probability transition matrices and temporal transition matrices. The influence of parameters is characterized by centroid transition processes within the same state partition. Experimental results demonstrate that the SDCNM method excels in modeling accuracy and, when combined with the TDLE-KNN decoder, enables high-precision flow field reconstruction. Comprehensive numerical experiments have demonstrated the outstanding accuracy, efficiency, robustness, and generalizability of the framework. The TDLE-KNN and SDCNM methods exhibit high compatibility, achieving precise flow field reconstruction even in the presence of noise, while maintaining stability in the case of incomplete data. Furthermore, the framework generalizes well to sparse or incomplete datasets, accurately predicting the system's behavior for unknown parameters, even when some parameters are missing.</p>

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Reduced-order complex network modeling of parametric fluid dynamic systems under partial observability

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Zihao Wang,
  • Guiyong Zhang,
  • Tiezhi Sun,
  • Zhe Sun,
  • Zhifan Zhang,
  • Bo Zhou

摘要

Understanding the nonlinear evolution of complex fluid dynamics systems under parameter variations has long been a significant challenge in both engineering and scientific fields. This paper addresses the problem of parameterized flow modeling for pitching airfoils under low Reynolds number and high angle-of-attack conditions. It combines time-delay embedding methods to tackle partial observability issues and utilizes complex network theory to transform data structures, proposing an innovative data-driven reduced-order modeling approach based on complex networks. The dimensionality reduction process employs the Time-Delay Laplacian Eigenmaps with K-Nearest Neighbors (TDLE-KNN) algorithm. This method effectively maps flow field data to a low-dimensional space, balancing high interpretability with low reconstruction error. Phase analysis reveals the latent dynamic characteristics of the system, where the evolution of phase angles reflects the system's inherent dynamics, and the variation in radial distances quantitatively describes the influence mechanism of system parameters. Furthermore, we have developed the Shared Dynamics Information Complex Network Modeling (SDCNM) framework, based on the assumption that multi-parameter systems share common latent dynamic characteristics. These shared features are represented in SDCNM through probability transition matrices and temporal transition matrices. The influence of parameters is characterized by centroid transition processes within the same state partition. Experimental results demonstrate that the SDCNM method excels in modeling accuracy and, when combined with the TDLE-KNN decoder, enables high-precision flow field reconstruction. Comprehensive numerical experiments have demonstrated the outstanding accuracy, efficiency, robustness, and generalizability of the framework. The TDLE-KNN and SDCNM methods exhibit high compatibility, achieving precise flow field reconstruction even in the presence of noise, while maintaining stability in the case of incomplete data. Furthermore, the framework generalizes well to sparse or incomplete datasets, accurately predicting the system's behavior for unknown parameters, even when some parameters are missing.