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

• URL: http://arxiv.org/abs/2510.24173v1
• Date: Tue, 28 Oct 2025 08:27:37 GMT
• Title: EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scale
• Authors: Yiheng Du, Aditi S. Krishnapriyan,
• Abstract summary: EddyFormer is a Transformer-based spectral-element architecture for large-scale turbulence simulation.<n>It achieves DNS-level accuracy at 2563 resolution, providing a 30x speedup over DNS.<n>It preserves accuracy on physics-invariant metrics-energy spectra, correlation functions, and structure functions-showing domain generalization.
• Score: 15.20548942455541
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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