用物理约束的Transformer模型,高效模拟三维湍流中小尺度结构。
PEST: Physics-Enhanced Swin Transformer for 3D Turbulence Simulation
- 基于窗口自注意力建模局部微分方程交互,兼顾精度与效率。
- 引入频域自适应损失,显著提升对高频小尺度结构的模拟精度。
- 融合纳维-斯托克斯残差与无散度正则化,确保物理一致性。
准确模拟湍流对科学与工程应用至关重要。直接数值模拟(DNS)虽具最高保真度,但计算成本过高;现有数据驱动方法在长期稳定滚动、物理一致性及小尺度结构再现方面表现不佳。这一问题在三维场景中尤为突出,因空间自由度呈立方增长,导致计算成本、内存需求和多尺度耦合难度急剧上升。为此,本文提出物理增强型Swin Transformer(PEST)用于三维湍流模拟。PEST采用基于窗口的自注意力机制,有效建模局部偏微分方程相互作用,同时保持计算效率。引入频域自适应损失,显式强化小尺度结构,提升高频动态模拟精度。为增强物理一致性,将纳维-斯托克斯残差约束与无散度正则化直接嵌入学习目标。在两个典型湍流配置上的大量实验表明,PEST实现了准确、物理一致且稳定的自回归长期模拟,优于现有数据驱动基线方法。
原文摘要 · Abstract (English)
Accurate simulation of turbulent flows is fundamental to scientific and engineering applications. Direct numerical simulation (DNS) offers the highest fidelity but is computationally prohibitive, while existing data-driven alternatives struggle with stable long-horizon rollouts, physical consistency, and faithful simulation of small-scale structures. These challenges are particularly acute in three-dimensional (3D) settings, where the cubic growth of spatial degrees of freedom dramatically amplifies computational cost, memory demand, and the difficulty of capturing multi-scale interactions. To address these challenges, we propose a Physics-Enhanced Swin Transformer (PEST) for 3D turbulence simulation. PEST leverages a window-based self-attention mechanism to effectively model localized PDE interactions while maintaining computational efficiency. We introduce a frequency-domain adaptive loss that explicitly emphasizes small-scale structures, enabling more faithful simulation of high-frequency dynamics. To improve physical consistency, we incorporate Navier--Stokes residual constraints and divergence-free regularization directly into the learning objective. Extensive experiments on two representative turbulent flow configurations demonstrate that PEST achieves accurate, physically consistent, and stable autoregressive long-term simulations, outperforming existing data-driven baselines.
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