arXiv:2505.19038cs.LGcs.AI2025-05被引 14

解决湍流长期预测中的高频信息丢失问题,提升物理真实性。

Turb-L1: Achieving Long-term Turbulence Tracing By Tackling Spectral Bias

  • 设计多网格架构与分层动力学合成机制,主动克服模型对低频成分的偏好。
  • 在二维湍流基准上,长期预测误差降低80.3%,结构相似性提升逾9倍。
  • 适合需要高保真流体模拟的科研与工程场景,如气候建模、航空设计。

准确预测湍流的长期演化对推动科学理解与优化工程应用至关重要。然而,现有深度学习方法在长期自回归预测中面临严重瓶颈,表现出过度平滑,难以精确追踪复杂流体动力学。我们对主流方法进行广泛实验与谱分析,揭示其根本缺陷源于谱偏差:模型在训练过程中倾向于关注低频平滑特征,忽视关键高频细节,导致保真度下降和物理失真。基于此洞察,我们提出Turb-L1,采用多网格架构中的分层动力学合成机制,显式克服谱偏差,精准捕捉跨尺度相互作用,保持高频动力学的保真度,实现可靠的长期湍流演化追踪。在2D湍流基准上的大量实验表明,Turb-L1表现优异:(I) 长期预测中,均方误差(MSE)降低80.3%,结构相似性(SSIM)提升超过9倍,显著提高预测保真度;(II) 有效克服谱偏差,准确再现全涡量谱,维持高波数区域的物理合理性,避免其他方法常见的谱失真或能量虚假积累。

原文摘要 · Abstract (English)

Accurately predicting the long-term evolution of turbulence is crucial for advancing scientific understanding and optimizing engineering applications. However, existing deep learning methods face significant bottlenecks in long-term autoregressive prediction, which exhibit excessive smoothing and fail to accurately track complex fluid dynamics. Our extensive experimental and spectral analysis of prevailing methods provides an interpretable explanation for this shortcoming, identifying Spectral Bias as the core obstacle. Concretely, spectral bias is the inherent tendency of models to favor low-frequency, smooth features while overlooking critical high-frequency details during training, thus reducing fidelity and causing physical distortions in long-term predictions. Building on this insight, we propose Turb-L1, an innovative turbulence prediction method, which utilizes a Hierarchical Dynamics Synthesis mechanism within a multi-grid architecture to explicitly overcome spectral bias. It accurately captures cross-scale interactions and preserves the fidelity of high-frequency dynamics, enabling reliable long-term tracking of turbulence evolution. Extensive experiments on the 2D turbulence benchmark show that Turb-L1 demonstrates excellent performance: (I) In long-term predictions, it reduces Mean Squared Error (MSE) by $80.3\%$ and increases Structural Similarity (SSIM) by over $9\times$ compared to the SOTA baseline, significantly improving prediction fidelity. (II) It effectively overcomes spectral bias, accurately reproducing the full enstrophy spectrum and maintaining physical realism in high-wavenumber regions, thus avoiding the spectral distortions or spurious energy accumulation seen in other methods.

湍流预测谱偏差多网格物理模型

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