用Transformer加速三维湍流模拟，30倍快于传统方法且保持高精度。
EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scale
- 基于谱元法构建Transformer架构，分离大尺度与小尺度流动特征。
- 在256³分辨率下达到DNS级精度，速度提升30倍，跨域泛化能力出色。
- 适用于复杂湍流场景，适合流体模拟、气候建模等需要高效计算的领域。
由于多尺度相互作用，直接数值模拟（DNS）完全解析湍流仍面临计算瓶颈。本文提出EddyFormer，一种基于Transformer的谱元法（SEM）架构，结合谱方法的精度与注意力机制的可扩展性。通过SEM分块将流动分解为网格尺度与亚网格尺度成分，有效捕捉局部与全局特征。构建新的三维各向同性湍流数据集，在256³分辨率下训练的EddyFormer实现接近DNS的精度，相较传统方法提速30倍。在超出训练范围4倍的未见域中，其物理不变量（能量谱、相关函数、结构函数）保持准确，展现良好泛化能力。在The Well基准测试中，成功模拟此前机器学习模型无法收敛的复杂流动，覆盖广泛物理条件下的动态行为。
原文摘要 · Abstract (English)
Computationally resolving turbulence remains a central challenge in fluid dynamics due to its multi-scale interactions. Fully resolving large-scale turbulence through direct numerical simulation (DNS) is computationally prohibitive, motivating data-driven machine learning alternatives. In this work, we propose EddyFormer, a Transformer-based spectral-element (SEM) architecture for large-scale turbulence simulation that combines the accuracy of spectral methods with the scalability of the attention mechanism. We introduce an SEM tokenization that decomposes the flow into grid-scale and subgrid-scale components, enabling capture of both local and global features. We create a new three-dimensional isotropic turbulence dataset and train EddyFormer to achieves DNS-level accuracy at 256^3 resolution, providing a 30x speedup over DNS. When applied to unseen domains up to 4x larger than in training, EddyFormer preserves accuracy on physics-invariant metrics-energy spectra, correlation functions, and structure functions-showing domain generalization. On The Well benchmark suite of diverse turbulent flows, EddyFormer resolves cases where prior ML models fail to converge, accurately reproducing complex dynamics across a wide range of physical conditions.
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