<p>This study investigates the efficacy of AutoEncoder (AE) neural networks in reducing the dimensionality of a heated turbulent channel flow subjected to Spanwise Wall Oscillations (SWO) at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\text {Re}_\tau = 200\)</EquationSource> </InlineEquation>. The dataset, generated using implicit Large Eddy Simulations (LES), comprises velocity and temperature fields at various oscillation amplitudes. Convolutional AutoEncoders (CAEs) are compared to the benchmark Proper Orthogonal Decomposition (POD) method to assess flow complexity and quantify improvements in reconstruction accuracy. <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta\)</EquationSource> </InlineEquation>-Variational AutoEncoders (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\beta\)</EquationSource> </InlineEquation>-VAEs) are employed to enhance the orthogonality of the latent samples, aiming to approach the uncorrelated modes of POD. The results demonstrate that CAEs consistently outperform POD in identifying a more compact coordinate system, capturing smaller flow scales with greater accuracy, especially for the wall-normal velocity component. Despite significant pruning of the latent variables, the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\beta\)</EquationSource> </InlineEquation>-VAE achieves a fine balance between the orthogonality of POD and the reconstruction capabilities of the CAE. Compared to POD, autoencoders provide superior separability of latent samples in two distinct aspects: (i) more effective amplitude separation, and (ii) more physically coherent phase separation. The CAE in particular leads to the best performance in both respects. This research highlights the potential of autoencoders in dimensionality reduction for complex turbulent flows and provides insights into the trade-off between reconstruction accuracy and latent-space interpretability.</p>

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Autoencoder-based dimensionality reduction of turbulent channel flow under spanwise wall oscillations

  • Lou Guérin,
  • Thomas Fisk,
  • Laurent Cordier,
  • Cédric Flageul,
  • Lionel Agostini

摘要

This study investigates the efficacy of AutoEncoder (AE) neural networks in reducing the dimensionality of a heated turbulent channel flow subjected to Spanwise Wall Oscillations (SWO) at \(\text {Re}_\tau = 200\) . The dataset, generated using implicit Large Eddy Simulations (LES), comprises velocity and temperature fields at various oscillation amplitudes. Convolutional AutoEncoders (CAEs) are compared to the benchmark Proper Orthogonal Decomposition (POD) method to assess flow complexity and quantify improvements in reconstruction accuracy. \(\beta\) -Variational AutoEncoders ( \(\beta\) -VAEs) are employed to enhance the orthogonality of the latent samples, aiming to approach the uncorrelated modes of POD. The results demonstrate that CAEs consistently outperform POD in identifying a more compact coordinate system, capturing smaller flow scales with greater accuracy, especially for the wall-normal velocity component. Despite significant pruning of the latent variables, the \(\beta\) -VAE achieves a fine balance between the orthogonality of POD and the reconstruction capabilities of the CAE. Compared to POD, autoencoders provide superior separability of latent samples in two distinct aspects: (i) more effective amplitude separation, and (ii) more physically coherent phase separation. The CAE in particular leads to the best performance in both respects. This research highlights the potential of autoencoders in dimensionality reduction for complex turbulent flows and provides insights into the trade-off between reconstruction accuracy and latent-space interpretability.