EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scale

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 $30\text{x}$ speedup over DNS. When applied to unseen domains up to $4\text{x}$ 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.