Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
143 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Synthetic Lagrangian Turbulence by Generative Diffusion Models (2307.08529v2)

Published 17 Jul 2023 in physics.flu-dyn, cond-mat.stat-mech, cs.CE, cs.LG, and nlin.CD

Abstract: Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, bio-fluids, atmosphere, oceans, and astrophysics. Despite exceptional theoretical, numerical, and experimental efforts conducted over the past thirty years, no existing models are capable of faithfully reproducing statistical and topological properties exhibited by particle trajectories in turbulence. We propose a machine learning approach, based on a state-of-the-art diffusion model, to generate single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, thereby bypassing the need for direct numerical simulations or experiments to obtain reliable Lagrangian data. Our model demonstrates the ability to reproduce most statistical benchmarks across time scales, including the fat-tail distribution for velocity increments, the anomalous power law, and the increased intermittency around the dissipative scale. Slight deviations are observed below the dissipative scale, particularly in the acceleration and flatness statistics. Surprisingly, the model exhibits strong generalizability for extreme events, producing events of higher intensity and rarity that still match the realistic statistics. This paves the way for producing synthetic high-quality datasets for pre-training various downstream applications of Lagrangian turbulence.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (90)
  1. Scalar turbulence. Nature 405, 639–646 (2000).
  2. Fluid particle accelerations in fully developed turbulence. Nature 409, 1017–1019 (2001).
  3. Measurement of lagrangian velocity in fully developed turbulence. Physical Review Letters 87, 214501 (2001).
  4. Particles and fields in fluid turbulence. Rev. Mod. Phys. 73, 913–975 (2001). URL https://link.aps.org/doi/10.1103/RevModPhys.73.913.
  5. Yeung, P. Lagrangian investigations of turbulence. Annual review of fluid mechanics 34, 115–142 (2002).
  6. Pomeau, Y. The long and winding road. Nature Physics 12, 198–199 (2016).
  7. Lessons from hydrodynamic turbulence. Physics Today 59, 43 (2006).
  8. Lagrangian properties of particles in turbulence. Annual review of fluid mechanics 41, 375–404 (2009).
  9. Shaw, R. A. Particle-turbulence interactions in atmospheric clouds. Annual Review of Fluid Mechanics 35, 183–227 (2003).
  10. Turbulence in the heavens. Nature Astronomy 5, 342–343 (2021).
  11. Persistent accelerations disentangle lagrangian turbulence. Nature Communications 10, 3550 (2019).
  12. A lagrangian view of turbulent dispersion and mixing. In Ten Chapters in Turbulance, 132–175 (Cambridge University Press, 2013).
  13. Lagrangian scale of particle dispersion in turbulence. Nature communications 4, 2013 (2013).
  14. Introduction to quantum turbulence. Proceedings of the National Academy of Sciences 111, 4647–4652 (2014).
  15. Xu, H. et al. Flight–crash events in turbulence. Proceedings of the National Academy of Sciences 111, 7558–7563 (2014).
  16. Laussy, F. P. Shining light on turbulence. Nature Photonics 17, 381–382 (2023).
  17. Frisch, U. Turbulence: the legacy of AN Kolmogorov (Cambridge University Press, 1995).
  18. Sawford, B. L. Reynolds number effects in Lagrangian stochastic models of turbulent dispersion. Phys. Fluids A: Fluid Dyn. 3, 1577–1586 (1991).
  19. Pope, S. B. Simple models of turbulent flows. Physics of Fluids 23, 011301 (2011).
  20. Viggiano, B. et al. Modelling lagrangian velocity and acceleration in turbulent flows as infinitely differentiable stochastic processes. Journal of Fluid Mechanics 900, A27 (2020).
  21. A conditionally cubic-gaussian stochastic lagrangian model for acceleration in isotropic turbulence. Journal of Fluid Mechanics 582, 423–448 (2007).
  22. Guidelines for the formulation of lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows. Physics of Fluids 26, 113303 (2014).
  23. Review of lagrangian stochastic models for trajectories in the turbulent atmosphere. Boundary-layer meteorology 78, 191–210 (1996).
  24. Conditional statistics for a passive scalar with a mean gradient and intermittency. Physics of Fluids 18 (2006).
  25. Elementary models for turbulent diffusion with complex physical features: eddy diffusivity, spectrum and intermittency. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, 20120184 (2013).
  26. Mimicking a turbulent signal: Sequential multiaffine processes. Physical Review E 57, R6261 (1998).
  27. Random cascades on wavelet dyadic trees. Journal of Mathematical Physics 39, 4142–4164 (1998).
  28. Log-infinitely divisible multifractal processes. Communications in Mathematical Physics 236, 449–475 (2003).
  29. On a skewed and multifractal unidimensional random field, as a probabilistic representation of kolmogorov’s views on turbulence. In Annales Henri Poincaré, vol. 20, 3693–3741 (Springer, 2019).
  30. Multi-level stochastic refinement for complex time series and fields: a data-driven approach. New Journal of Physics 23, 063063 (2021).
  31. Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in fourier and wavelet space. Journal of Physics: Complexity (2022).
  32. Zamansky, R. Acceleration scaling and stochastic dynamics of a fluid particle in turbulence. Physical Review Fluids 7, 084608 (2022).
  33. Arnéodo, A. et al. Universal intermittent properties of particle trajectories in highly turbulent flows. Physical Review Letters 100, 254504 (2008).
  34. Auto-Encoding Variational Bayes. In 2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings (2014). eprint http://arxiv.org/abs/1312.6114v10.
  35. Goodfellow, I. et al. Generative adversarial nets. Advances in neural information processing systems 27 (2014).
  36. Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems 33, 6840–6851 (2020).
  37. Diffusion models beat gans on image synthesis. Advances in Neural Information Processing Systems 34, 8780–8794 (2021).
  38. van den Oord, A. et al. WaveNet: A Generative Model for Raw Audio. In Proc. 9th ISCA Workshop on Speech Synthesis Workshop (SSW 9), 125 (2016).
  39. Brown, T. et al. Language models are few-shot learners. Advances in neural information processing systems 33, 1877–1901 (2020).
  40. Synthetic data in machine learning for medicine and healthcare. Nature Biomedical Engineering 5, 493–497 (2021).
  41. Turbulence modeling in the age of data. Annual review of fluid mechanics 51, 357–377 (2019).
  42. Machine learning for fluid mechanics. Annual review of fluid mechanics 52, 477–508 (2020).
  43. Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, 20170844 (2018).
  44. Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach. Physical review letters 120, 024102 (2018).
  45. Spatio-temporal deep learning models of 3d turbulence with physics informed diagnostics. Journal of Turbulence 21, 484–524 (2020).
  46. Deep unsupervised learning of turbulence for inflow generation at various reynolds numbers. Journal of Computational Physics 406, 109216 (2020).
  47. Guastoni, L. et al. Convolutional-network models to predict wall-bounded turbulence from wall quantities. Journal of Fluid Mechanics 928, A27 (2021).
  48. Reconstruction of turbulent data with deep generative models for semantic inpainting from turb-rot database. Physical Review Fluids 6, 050503 (2021).
  49. A deep-learning approach for reconstructing 3d turbulent flows from 2d observation data. Scientific Reports 13, 2529 (2023).
  50. A physics-informed diffusion model for high-fidelity flow field reconstruction. Journal of Computational Physics 478, 111972 (2023).
  51. Buzzicotti, M. Data reconstruction for complex flows using ai: recent progress, obstacles, and perspectives. Europhysics Letters (2023).
  52. Granero-Belinchon, C. Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statistics. Physica D: Nonlinear Phenomena 458, 133997 (2024).
  53. Improved denoising diffusion probabilistic models. In International Conference on Machine Learning, 8162–8171 (PMLR, 2021).
  54. Chevillard, L. et al. Lagrangian velocity statistics in turbulent flows: Effects of dissipation. Physical review letters 91, 214502 (2003).
  55. Biferale, L. et al. Multifractal statistics of lagrangian velocity and acceleration in turbulence. Physical review letters 93, 064502 (2004).
  56. Deep unsupervised learning using nonequilibrium thermodynamics. In International Conference on Machine Learning, 2256–2265 (PMLR, 2015).
  57. Accurate and conservative estimates of mrf log-likelihood using reverse annealing. In Artificial Intelligence and Statistics, 102–110 (PMLR, 2015).
  58. Long time correlations in lagrangian dynamics: a key to intermittency in turbulence. Physical review letters 89, 254502 (2002).
  59. Multitime structure functions and the lagrangian scaling of turbulence. Physical Review Fluids 7, 064603 (2022).
  60. Varieties of dynamic multiscaling in fluid turbulence. Physical review letters 93, 024501 (2004).
  61. Temporal multiscaling in hydrodynamic turbulence. Physical Review E 55, 7030 (1997).
  62. Borgas, M. The multifractal lagrangian nature of turbulence. Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences 342, 379–411 (1993).
  63. Nelkin, M. Multifractal scaling of velocity derivatives in turbulence. Physical Review A 42, 7226 (1990).
  64. Degrees of freedom of turbulence. Physical Review A 35, 1971 (1987).
  65. Meneveau, C. Transition between viscous and inertial-range scaling of turbulence structure functions. Physical Review E 54, 3657 (1996).
  66. Benzi, R. et al. A random process for the construction of multiaffine fields. Physica D: Nonlinear Phenomena 65, 352–358 (1993).
  67. Wavelet score-based generative modeling. Advances in Neural Information Processing Systems 35, 478–491 (2022).
  68. Two-particle dispersion in isotropic turbulent flows. Annual review of fluid mechanics 41, 405–432 (2009).
  69. Extreme events in the dispersions of two neighboring particles under the influence of fluid turbulence. Physical review letters 109, 144501 (2012).
  70. Biferale, L. et al. Multiparticle dispersion in fully developed turbulence. Physics of Fluids 17, 111701 (2005).
  71. The pirouette effect in turbulent flows. Nature Physics 7, 709–712 (2011).
  72. Roemmich, D. et al. On the future of argo: A global, full-depth, multi-disciplinary array. Frontiers in Marine Science 6, 439 (2019).
  73. On characterizing ocean kinematics from surface drifters. Journal of Atmospheric and Oceanic Technology 39, 1183–1198 (2022).
  74. Turb-lagr. a database of 3d lagrangian trajectories in homogeneous and isotropic turbulence. arXiv:2303.08662 (2023).
  75. Optimal tracking strategies in a turbulent flow. Communications Physics 6, 256 (2023).
  76. On the efficiency and accuracy of interpolation methods for spectral codes. SIAM journal on scientific computing 34, B479–B498 (2012).
  77. U-net: Convolutional networks for biomedical image segmentation. In Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part III 18, 234–241 (Springer, 2015).
  78. Vaswani, A. et al. Attention is all you need. Advances in neural information processing systems 30 (2017).
  79. Denoising diffusion implicit models. In International Conference on Learning Representations (2021). URL https://openreview.net/forum?id=St1giarCHLP.
  80. Lu, C. et al. Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. Advances in Neural Information Processing Systems 35, 5775–5787 (2022).
  81. Dataset for: Synthetic lagrangian turbulence by generative diffusion models. Data set (2024). URL http://doi.org/10.15161/oar.it/143615.
  82. Smartturb/diffusion-lagr: stable (2024). URL https://doi.org/10.5281/zenodo.10563386.
  83. Supplementary code for: Synthetic lagrangian turbulence by generative diffusion models (2024). URL https://codeocean.com/capsule/0870187/tree/v1. CodeOcean.
  84. Experimental and numerical study of the lagrangian dynamics of high reynolds turbulence. New Journal of Physics 6, 116 (2004).
  85. Lagrangian statistics of navier–stokes and mhd turbulence. Journal of Plasma Physics 73, 821–830 (2007).
  86. Particle trapping in three-dimensional fully developed turbulence. Physics of Fluids 17, 021701 (2005).
  87. Fisher, R. T. et al. Terascale turbulence computation using the flash3 application framework on the ibm blue gene/l system. IBM Journal of Research and Development 52, 127–136 (2008).
  88. Reynolds number dependence of lagrangian statistics in large numerical simulations of isotropic turbulence. Journal of Turbulence N58 (2006).
  89. High order lagrangian velocity statistics in turbulence. Physical review letters 96, 024503 (2006).
  90. Backwards and forwards relative dispersion in turbulent flow: an experimental investigation. Physical Review E 74, 016304 (2006).
Citations (20)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Github Logo Streamline Icon: https://streamlinehq.com

GitHub

  1. GitHub - SmartTURB/diffusion-lagr: Synthetic Lagrangian Turbulence by Generative Diffusion Models (24 stars)
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets