Title: EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scale Show Chinese title

Title: EddyFormer：大规模三维湍流的加速神经模拟

Abstract: 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. Show Chinese abstract

Abstract: 计算上解决湍流仍然是流体力学中的一个核心挑战，因为其涉及多尺度相互作用。 通过直接数值模拟（DNS）完全解析大尺度湍流在计算上是不可行的，这促使了数据驱动的机器学习替代方法。 在本工作中，我们提出了EddyFormer，一种基于Transformer的谱元（SEM）架构，用于大规模湍流模拟，该架构结合了谱方法的准确性与注意力机制的可扩展性。 我们引入了一种SEM分词方法，将流动分解为网格尺度和亚网格尺度成分，从而能够捕捉局部和全局特征。 我们创建了一个新的三维各向同性湍流数据集，并训练EddyFormer在256^3分辨率下达到DNS级别的准确性，相比DNS提供了30倍的速度提升。 当应用于比训练时大4倍的未知领域时，EddyFormer在物理不变度量——能量谱、相关函数和结构函数上保持准确性，展示了领域泛化能力。 在多样湍流流动的Well基准套件上，EddyFormer解决了先前ML模型无法收敛的情况，在广泛的物理条件下准确再现了复杂的动力学。