mlsanityData to 14 Oct 2026

Towards Physics-informed Deep Learning for Turbulent Flow Prediction

arXiv 1911.08655 ↗First posted 20 Nov 2019physics.comp-ph cs.LG stat.MLcited by 204

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Abstract (arXiv)

While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim to predict turbulent flow by learning its highly nonlinear dynamics from spatiotemporal velocity fields of large-scale fluid flow simulations of relevance to turbulence modeling and climate modeling. We adopt a hybrid approach by marrying two well-established turbulent flow simulation techniques with deep learning. Specifically, we introduce trainable spectral filters in a coupled model of Reynolds-averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES), followed by a specialized U-net for prediction. Our approach, which we call turbulent-Flow Net (TF-Net), is grounded in a principled physics model, yet offers the flexibility of learned representations. We compare our model, TF-Net, with state-of-the-art baselines and observe significant reductions in error for predictions 60 frames ahead. Most importantly, our method predicts physical fields that obey desirable physical characteristics, such as conservation of mass, whilst faithfully emulating the turbulent kinetic energy field and spectrum, which are critical for accurate prediction of turbulent flows.

Key facts. Cited by 204 papers in the map (data through 14 Oct 2026). First posted on arXiv 20 Nov 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 37; 2022: 54; 2023: 46; 2024: 24; 2025: 27; 2026: 16.

204 papers.

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  1. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  2. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 473
  3. 2021Machine learning accelerated computational fluid dynamicscited by 471
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  8. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 197
  9. 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstructioncited by 152
  10. 2021Enhancing Computational Fluid Dynamics with Machine Learningcited by 138
  11. 2023Scalable Transformer for PDE Surrogate Modelingcited by 128
  12. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
38 more
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  2. 2022Monarch: Expressive Structured Matrices for Efficient and Accurate Trainingcited by 106
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  5. 2021Learned Coarse Models for Efficient Turbulence Simulationcited by 91
  6. 2023Solving High-Dimensional PDEs with Latent Spectral Modelscited by 89
  7. 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 84
  8. 2022AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutionscited by 82
  9. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 75
  10. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulationcited by 71
  11. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 65
  12. 2021Encoding physics to learn reaction-diffusion processescited by 61
  13. 2023On the Connection Between MPNN and Graph Transformercited by 61
  14. 2022Learning to correct spectral methods for simulating turbulent flowscited by 49
  15. 2023From Zero to Turbulence: Generative Modeling for 3D Flow Simulationcited by 49
  16. 2022STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Predictioncited by 45
  17. 2023Group Equivariant Fourier Neural Operators for Partial Differential Equationscited by 45
  18. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 44
  19. 2022Mitigating spectral bias for the multiscale operator learningcited by 44
  20. 2022Learning to Accelerate Partial Differential Equations via Latent Global Evolutioncited by 39
  21. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 38
  22. 2023Learning Neural PDE Solvers with Parameter-Guided Channel Attentioncited by 38
  23. 2024A Library for Learning Neural Operatorscited by 38
  24. 2022Physical Design using Differentiable Learned Simulatorscited by 37
  25. 2022Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problemscited by 34
  26. 2024TimeDiT: General-purpose Diffusion Transformers for Time Series Foundation Modelcited by 33
  27. 2025Mitigating Spectral Bias in Neural Operators via High-Frequency Scaling for Physical Systemscited by 31
  28. 2022Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamicscited by 30
  29. 2023Koopman neural operator as a mesh-free solver of non-linear partial differential equationscited by 29
  30. 2022MAgNet: Mesh Agnostic Neural PDE Solvercited by 28
  31. 2021Constraint-based graph network simulatorcited by 27
  32. 2024AirPhyNet: Harnessing Physics-Guided Neural Networks for Air Quality Predictioncited by 26
  33. 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
  34. 2022Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learningcited by 24
  35. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  36. 2023Lie Point Symmetry and Physics Informed Networkscited by 24
  37. 2024HAMLET: Graph Transformer Neural Operator for Partial Differential Equationscited by 24
  38. 2023A Neural PDE Solver with Temporal Stencil Modelingcited by 22

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