arXiv:2606.11691cs.LGphysics.flu-dyn2026-06中稿 · ICML

通过频谱正则化改进生成湍流的隐空间表示,显著提升高耗散区能量保留。

Spectrally Regularized Latent Flow Matching for Turbulence Generation

论文配图:Spectrally Regularized Latent Flow Matching for Turbulence Generation
图 1 · 摘自论文原文
  • 设计频谱加权损失函数,重构和生成时保留94%与79%的高耗散区能量
  • 新方法在20次函数求值下实现DD偏差-0.117,远优于原方法的-0.70上限
  • 适合关注湍流生成质量、频谱保真度的流体模拟研究者

隐空间扩散与流匹配已成为合成湍流生成的主流方法,但普遍存在高耗散区能量低估问题。本文提出一种频谱正则化的隐空间流匹配框架,通过引入区域加权对数频谱目标函数,直接解决该缺陷。在雷诺数约2250的256²分辨率直接数值模拟(DNS)数据集上,将原始基于MSE训练的变分自编码器(VAE)替换为频谱正则化模型后,重建时深层耗散区保留的谱功率从25%提升至94%,无条件生成时从20%提升至79%。改进后的隐空间还带来更优的采样成本-精度权衡:原方法存在不可逾越的质量天花板(DD偏差-0.70),而新方法仅用20次函数评估即达DD偏差-0.117。机制分析表明,性能提升主要源于编码器驱动的隐空间重组织,而非解码器容量;对比实验显示,MSE模型表现为保守抑制型,通过削弱间歇性高波数结构来最小化逐点误差。两种方法均恢复了二阶结构函数及S₃符号,表明正确级联方向无需显式监督。但S₃幅度仍存微小差距,提示相位相干三元组织是未来模型需补充的关键维度。

原文摘要 · Abstract (English)

Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes. We introduce a latent flow matching framework with a spectrally regularized compression stage that directly targets this failure mode. On a 256^2 DNS dataset at Re_f \approx 2250, replacing an MSE-trained VAE with a zone-weighted log-spectral objective raises deep-dissipation retained spectral power from 25% to 94% in reconstruction and from 20% to 79% in unconditional generation. The improved latent representation also yields a substantially better sampling cost-fidelity tradeoff: the MSE-trained latent space imposes a fundamental quality ceiling near DD bias -0.70 that no integrator or step-count can overcome, while the spectrally regularized latent space reaches DD bias -0.117 at just 20 function evaluations. Mechanistically, encoder-decoder swap experiments show that the improvement is driven primarily by encoder-induced latent reorganization rather than decoder capacity, while a support-amplitude decomposition reveals that MSE-trained models behave as conservative suppression models, minimizing pointwise error by attenuating intermittent high-wavenumber structure. Both pipelines recover the second-order structure function and the correct sign of S_3, indicating the correct cascade direction without explicit supervision. A small residual gap in the magnitude of S_3 suggests that phase-coherent triadic organization remains a complementary axis to amplitude fidelity for future generative turbulence models.

湍流生成隐空间建模频谱正则流匹配

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