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<p>Accurate reconstruction of unsteady wake flow fields is essential for understanding vortex shedding dynamics and for enabling data-efficient analysis in engineering applications. This research proposes a spatiotemporal reconstruction framework based on a Particle Swarm Optimization–Convolutional Neural Network–Long Short-Term Memory (PSO-CNN-LSTM) architecture for two-dimensional incompressible cylindrical wake flows. The convolutional encoder extracts local spatial features from velocity snapshots, the long short-term memory module models temporal evolution and phase information of vortex shedding, and particle swarm optimization automatically searches key hyperparameters to reduce empirical tuning. To evaluate generalization under missing-frame reconstruction, each target snapshot is excluded from training and is reconstructed using only its preceding history frames. In addition, continuous rolling prediction is performed over the last ten steps (49.1–50.0&#xa0;s) to investigate error accumulation behaviors. Results show that the proposed method reconstructs dominant wake structures with high fidelity. For missing-frame reconstruction at multiple target times, the streamwise velocity error remains at the order of 10<sup>–3</sup>, while the cross-stream velocity error is at the order of 10<sup>–2</sup>, indicating that cross-stream dynamics are more challenging due to their stronger dependence on vortex-shedding phase. Compared with LSTM, RNN and Transformer baselines in the ten-step rolling prediction, PSO-CNN-LSTM achieves markedly lower errors for the streamwise component and improved overall stability. Furthermore, an uncertainty quantification strategy based on Monte Carlo dropout is introduced, yielding pixel-wise predictive mean and standard deviation. The error–uncertainty coupling analysis demonstrates positive correlations between absolute error and predicted uncertainty. These findings indicate that the proposed framework not only improves reconstruction accuracy but also provides reliable spatial indicators of potential mismatch regions, supporting trustworthy flow-field reconstruction in unsteady wake flows.</p>

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A flow field reconstruction based on cylindrical wake flow data using the PSO-CNN-LSTM algorithm

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月24日

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  • Qingtong Liu,
  • Dongxin Xu,
  • Min Xu,
  • Shuo Ma

摘要

Accurate reconstruction of unsteady wake flow fields is essential for understanding vortex shedding dynamics and for enabling data-efficient analysis in engineering applications. This research proposes a spatiotemporal reconstruction framework based on a Particle Swarm Optimization–Convolutional Neural Network–Long Short-Term Memory (PSO-CNN-LSTM) architecture for two-dimensional incompressible cylindrical wake flows. The convolutional encoder extracts local spatial features from velocity snapshots, the long short-term memory module models temporal evolution and phase information of vortex shedding, and particle swarm optimization automatically searches key hyperparameters to reduce empirical tuning. To evaluate generalization under missing-frame reconstruction, each target snapshot is excluded from training and is reconstructed using only its preceding history frames. In addition, continuous rolling prediction is performed over the last ten steps (49.1–50.0 s) to investigate error accumulation behaviors. Results show that the proposed method reconstructs dominant wake structures with high fidelity. For missing-frame reconstruction at multiple target times, the streamwise velocity error remains at the order of 10–3, while the cross-stream velocity error is at the order of 10–2, indicating that cross-stream dynamics are more challenging due to their stronger dependence on vortex-shedding phase. Compared with LSTM, RNN and Transformer baselines in the ten-step rolling prediction, PSO-CNN-LSTM achieves markedly lower errors for the streamwise component and improved overall stability. Furthermore, an uncertainty quantification strategy based on Monte Carlo dropout is introduced, yielding pixel-wise predictive mean and standard deviation. The error–uncertainty coupling analysis demonstrates positive correlations between absolute error and predicted uncertainty. These findings indicate that the proposed framework not only improves reconstruction accuracy but also provides reliable spatial indicators of potential mismatch regions, supporting trustworthy flow-field reconstruction in unsteady wake flows.