mlsanityData to 7 Oct 2026

Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equations

arXiv 2306.01174 ↗First posted 1 Jun 2023cs.LG cs.NA math.NAcited by 13

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Abstract (arXiv)

We introduce a data-driven learning framework that assimilates two powerful ideas: ideal large eddy simulation (LES) from turbulence closure modeling and neural stochastic differential equations (SDE) for stochastic modeling. The ideal LES models the LES flow by treating each full-order trajectory as a random realization of the underlying dynamics, as such, the effect of small-scales is marginalized to obtain the deterministic evolution of the LES state. However, ideal LES is analytically intractable. In our work, we use a latent neural SDE to model the evolution of the stochastic process and an encoder-decoder pair for transforming between the latent space and the desired ideal flow field. This stands in sharp contrast to other types of neural parameterization of closure models where each trajectory is treated as a deterministic realization of the dynamics. We show the effectiveness of our approach (niLES - neural ideal LES) on a challenging chaotic dynamical system: Kolmogorov flow at a Reynolds number of 20,000. Compared to competing methods, our method can handle non-uniform geometries using unstructured meshes seamlessly. In particular, niLES leads to trajectories with more accurate statistics and enhances stability, particularly for long-horizon rollouts.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 27 of its 82 references that are in the map. First posted on arXiv 1 Jun 2023.

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27 of 82 references.

References · 27

  1. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2018On the Spectral Bias of Neural Networkscited by 1,321
  4. 2021Multiscale Vision Transformerscited by 896
  5. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  6. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
  7. 2021MViTv2: Improved Multiscale Vision Transformers for Classification and Detectioncited by 516
  8. 2021Machine learning accelerated computational fluid dynamicscited by 461
  9. 2022Message Passing Neural PDE Solverscited by 368
  10. 2022On Neural Differential Equationscited by 264
  11. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
  12. 2019Towards Physics-informed Deep Learning for Turbulent Flow Predictioncited by 203
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  1. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
  2. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  3. 2022Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecastcited by 164
  4. 2021Neural SDEs as Infinite-Dimensional GANscited by 159
  5. 2021Learned Coarse Models for Efficient Turbulence Simulationcited by 90
  6. 2021Efficient and Accurate Gradients for Neural SDEscited by 68
  7. 2022Learning to correct spectral methods for simulating turbulent flowscited by 49
  8. 2022Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizonscited by 39
  9. 2021Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equationscited by 38
  10. 2020A Perspective on Machine Learning Methods in Turbulence Modellingcited by 22
  11. 2018Data-driven Discovery of Closure Modelscited by 19
  12. 2018A machine learning framework for data driven acceleration of computations of differential equationscited by 18
  13. 2021Embedded training of neural-network sub-grid-scale turbulence modelscited by 13
  14. 2022Long-term stability and generalization of observationally-constrained stochastic data-driven models for geophysical turbulencecited by 8
  15. 2021Computing foaming flows across scales: from breaking waves to microfluidicscited by 2

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Citing papers per year: 2023: 2; 2024: 3; 2025: 5; 2026: 3.

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  4. 2025EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scalecited by 6
  5. 2024A probabilistic framework for learning non-intrusive corrections to long-time climate simulations from short-time training datacited by 5
  6. 2025Learning Stochastic Multiscale Modelscited by 3
  7. 2025AutoHood3D: A Multi-Modal Benchmark for Automotive Hood Design and Fluid-Structure Interactioncited by 3
  8. 2025Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modelingcited by 2
  9. 2026Learning Permutation-invariant Macroscopic Dynamicscited by 1
  10. 2023Attention-enhanced neural differential equations for physics-informed deep learning of ion transportcited by 0
  11. 2025Scalable learning of macroscopic stochastic dynamicscited by 0
  12. 2026Improving Infinitely Deep Bayesian Neural Networks with Nesterov's Accelerated Gradient Methodcited by 0
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