arXiv:2507.22082cs.LGcs.AI2025-07被引 1

用局部块重建湍流流场,实现三维超分辨率,速度快且参数少。

Patch-Based 3D Variational Autoencoder for Super-Resolution of Turbulent Channel Flow

  • 分块3D变分自编码器,用局部高分辨率块反推全局细节
  • 误差比双三次和兰乔斯插值低27%-30%,频域误差降为三分之一
  • 适合处理高雷诺数湍流模拟数据,尤其适用于粗网格有限元结果

直接数值模拟(DNS)能精确解析壁面湍流的所有时空尺度,但随雷诺数升高成本剧增。超分辨率(SR)通过从粗略场重建细粒度结构提供实用替代方案。现有方法多集中于二维数据,因缺乏涡拉伸效应,难以推广至三维,且模型复杂度随重构体积增长。本文提出基于块的三维变分自编码器(3D-VAE),从更大范围的粗网格邻域重建16³的局部高分辨率块。学习到的算子以卷积方式在全域应用并叠加平均,使参数量仅依赖于块大小而非域大小。模型在约翰霍普金斯湍流数据库中雷诺数约1000的单个DNS快照上训练,并在保留快照上评估。相比DNS,该方法均方绝对误差为0.055,优于双三次(0.075)和兰乔斯(0.076)插值。频域中,二维傅里叶振幅均方绝对误差由2.63和2.85降至0.91,改善约三倍。应用于粗网格有限元模拟时,可重建输入缺失的谱成分,展现超越滤波DNS的迁移能力。同一数据集训练的条件3D-GAN在Wasserstein训练下未能收敛,作为负例报告。主要局限包括最小可分辨尺度衰减、块步长引起的周期性伪影,以及极端速度值预测偏低。

原文摘要 · Abstract (English)

Direct numerical simulation (DNS) accurately resolves all spatio-temporal scales of wall-bounded turbulence but becomes prohibitively expensive as the Reynolds number increases. Super-resolution (SR) provides a practical alternative by reconstructing fine-scale flow structures from coarse fields. Most existing SR methods focus on two-dimensional data, where vortex stretching is absent, and extend poorly to three dimensions because model complexity increases with the reconstructed volume. We propose a patch-based three-dimensional variational autoencoder (3D-VAE) that reconstructs a local (16^3) high-resolution block from a larger coarse neighbourhood. The learned operator is then applied convolutionally across the domain with overlap averaging, making the parameter count dependent only on patch size rather than domain size. The model is trained using the streamwise velocity from a single DNS snapshot of turbulent channel flow at (Re_τ\approx 1000) from the Johns Hopkins Turbulence Database and evaluated on a held-out snapshot. Compared with DNS, the proposed method achieves a mean absolute error of 0.055, outperforming tricubic (0.075) and Lanczos (0.076) interpolation. In spectral space, it reduces the mean absolute error of the two-dimensional Fourier amplitude from 2.63 and 2.85 to 0.91, an improvement of about threefold. Applied to coarse finite-element simulations, the model reconstructs spectral content absent from the input, demonstrating transfer beyond filtered DNS. A conditional 3D-GAN trained on the same data failed to converge under Wasserstein training and is reported as a negative result. The main limitations are attenuation of the smallest resolved scales, periodic artefacts caused by the patch stride, and under-prediction of extreme velocity values.

超分辨率湍流模拟3D生成模型

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