mlsanityData to 14 Oct 2026

Learned Coarse Models for Efficient Turbulence Simulation

arXiv 2112.15275 ↗First posted 31 Dec 2021physics.flu-dyn cs.LG physics.comp-phcited by 91

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Abstract (arXiv)

Turbulence simulation with classical numerical solvers requires high-resolution grids to accurately resolve dynamics. Here we train learned simulators at low spatial and temporal resolutions to capture turbulent dynamics generated at high resolution. We show that our proposed model can simulate turbulent dynamics more accurately than classical numerical solvers at the comparably low resolutions across various scientifically relevant metrics. Our model is trained end-to-end from data and is capable of learning a range of challenging chaotic and turbulent dynamics at low resolution, including trajectories generated by the state-of-the-art Athena++ engine. We show that our simpler, general-purpose architecture outperforms various more specialized, turbulence-specific architectures from the learned turbulence simulation literature. In general, we see that learned simulators yield unstable trajectories; however, we show that tuning training noise and temporal downsampling solves this problem. We also find that while generalization beyond the training distribution is a challenge for learned models, training noise, added loss constraints, and dataset augmentation can help. Broadly, we conclude that our learned simulator outperforms traditional solvers run on coarser grids, and emphasize that simple design choices can offer stability and robust generalization.

Key facts. Cited by 91 papers in the map (data through 14 Oct 2026). Builds on 29 of its 61 references that are in the map. First posted on arXiv 31 Dec 2021.

Builds on

29 of 61 references.

References · 29

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17 more
  1. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
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Citing papers per year: 2022: 13; 2023: 23; 2024: 19; 2025: 16; 2026: 20.

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  1. 2022PDEBENCH: An Extensive Benchmark for Scientific Machine Learningcited by 413
  2. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
  3. 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstructioncited by 152
  4. 2023Scalable Transformer for PDE Surrogate Modelingcited by 128
  5. 2022MultiScale MeshGraphNetscited by 98
  6. 2023Multiple Physics Pretraining for Physical Surrogate Modelscited by 98
  7. 2022Clifford Neural Layers for PDE Modelingcited by 92
  8. 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 91
  9. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulationcited by 71
  10. 2023Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformerscited by 57
  11. 2024CViT: Continuous Vision Transformer for Operator Learningcited by 51
  12. 2022Learning to correct spectral methods for simulating turbulent flowscited by 49
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  1. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 49
  2. 2022Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizonscited by 39
  3. 2024AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fieldscited by 39
  4. 2023Learning Neural PDE Solvers with Parameter-Guided Channel Attentioncited by 38
  5. 2022Physical Design using Differentiable Learned Simulatorscited by 37
  6. 2022A posteriori learning for quasi-geostrophic turbulence parametrizationcited by 36
  7. 2024DySLIM: Dynamics Stable Learning by Invariant Measure for Chaotic Systemscited by 30
  8. 2022MAgNet: Mesh Agnostic Neural PDE Solvercited by 28
  9. 2024Universal Physics Transformers: A Framework For Efficiently Scaling Neural Operatorscited by 27
  10. 2024Differentiability in Unrolled Training of Neural Physics Simulators on Transient Dynamicscited by 27
  11. 2024Text2PDE: Latent Diffusion Models for Accessible Physics Simulationcited by 25
  12. 2025Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networkscited by 25
  13. 2023A Neural PDE Solver with Temporal Stencil Modelingcited by 22
  14. 2025Erwin: A Tree-based Hierarchical Transformer for Large-scale Physical Systemscited by 22
  15. 2025Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaoscited by 21
  16. 2022Meta-PDE: Learning to Solve PDEs Quickly Without a Meshcited by 18
  17. 2023Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformercited by 18
  18. 2024PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systemscited by 18
  19. 2023BubbleML: A Multi-Physics Dataset and Benchmarks for Machine Learningcited by 17
  20. 2024Adversarial Learning for Neural PDE Solvers with Sparse Datacited by 16
  21. 2025Force-Free Molecular Dynamics Through Autoregressive Equivariant Networkscited by 15
  22. 2023Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systemscited by 14
  23. 2024SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equationscited by 14
  24. 2023Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equationscited by 13
  25. 2024P2C2Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamicscited by 13
  26. 2023Multi-Scale Message Passing Neural PDE Solverscited by 12
  27. 2023Fluid Simulation on Neural Flow Mapscited by 12
  28. 2023Coupled Multiwavelet Neural Operator Learning for Coupled Partial Differential Equationscited by 11
  29. 2025Binned Spectral Power Loss for Improved Prediction of Chaotic Systemscited by 10
  30. 2024Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogatescited by 8
  31. 2023Invariant preservation in machine learned PDE solvers via error correctioncited by 7
  32. 2023Equivariant Neural Simulators for Stochastic Spatiotemporal Dynamicscited by 6
  33. 2025Neural Emulator Superiority: When Machine Learning for PDEs Surpasses its Training Datacited by 6
  34. 2023Gradient-free online learning of subgrid-scale dynamics with neural emulatorscited by 5
  35. 2025Discovering Physics Laws of Dynamical Systems via Invariant Function Learningcited by 5
  36. 2025PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systemscited by 5
  37. 2025SlotPi: Physics-informed Object-centric Reasoning Modelscited by 5
  38. 2023Adaptive learning of effective dynamics: Adaptive real-time, online modeling for complex systemscited by 4

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