EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scale
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| Format: | Preprint |
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2025
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| _version_ | 1866917047896637440 |
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| author | Du, Yiheng Krishnapriyan, Aditi S. |
| author_facet | Du, Yiheng Krishnapriyan, Aditi S. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_24173 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scale Du, Yiheng Krishnapriyan, Aditi S. Machine Learning Numerical Analysis Dynamical Systems Fluid Dynamics 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. |
| title | EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scale |
| topic | Machine Learning Numerical Analysis Dynamical Systems Fluid Dynamics |
| url | https://arxiv.org/abs/2510.24173 |