Turbulence scaling from deep learning diffusion generative models. (English) Zbl 07899008
Summary: Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehension necessitates an understanding of the space of turbulent fluid flow configurations. We employ a diffusion-based generative model to learn the distribution of turbulent vorticity profiles and generate snapshots of turbulent solutions to the incompressible Navier-Stokes equations. We consider the inverse cascade in two spatial dimensions and generate diverse turbulent solutions that differ from those in the training dataset. We analyze the statistical scaling properties of the new turbulent profiles, calculate their structure functions, energy power spectrum, velocity probability distribution function and moments of local energy dissipation. All the learnt scaling exponents are consistent with the expected Kolmogorov scaling This agreement with established turbulence characteristics provides strong evidence of the model’s capability to capture essential features of real-world turbulence.
References:
| [1] | R. Apte, S. Nidhan, R. Ranade, J. Pathak, Diffusion model based data generation for partial differential equations, 2023. |
| [2] | Benzi, R.; Ciliberto, S.; Baudet, C.; Chavarria, G. R., On the scaling of three-dimensional homogeneous and isotropic turbulence, Phys. D: Nonlinear Phenom., 80, 385-398, 1995 · Zbl 0899.76196 |
| [3] | Biferale, L.; Bonaccorso, F.; Buzzicotti, M.; Iyer, K. P., Self-similar subgrid-scale models for inertial range turbulence and accurate measurements of intermittency, Phys. Rev. Lett., 123, 1, jul 2019 |
| [4] | Boffetta, G.; Ecke, R. E., Two-dimensional turbulence, Annu. Rev. Fluid Mech., 44, 1, 427-451, 2012 · Zbl 1350.76022 |
| [5] | Boffetta, G.; Musacchio, S., Evidence for the double cascade scenario in two-dimensional turbulence, Phys. Rev. E, 82, Article 016307 pp., Jul 2010 |
| [6] | Buzzicotti, M.; Bonaccorso, F., Inferring turbulent environments via machine learning, Eur. Phys. J. E, 45, 12, 102, Dec 2022 |
| [7] | Canuto, C.; Hussaini, M.; Quarteroni, A.; Zang, T., Spectral methods, evolution to complex geometries and applications to fluid dynamics, vol. 01, 2007 · Zbl 1121.76001 |
| [8] | Chen, S. Y.; Dhruva, B.; Kurien, S.; Sreenivasan, K. R.; Taylor, M. A., Anomalous scaling of low-order structure functions of turbulent velocity, J. Fluid Mech., 533, 183-192, 2005 · Zbl 1074.76030 |
| [9] | Di Leoni, P. Clark; Mazzino, A.; Biferale, L., Inferring flow parameters and turbulent configuration with physics-informed data assimilation and spectral nudging, Phys. Rev. Fluids, 3, Article 104604 pp., Oct 2018 |
| [10] | Drygala, C.; Winhart, B.; di Mare, F.; Gottschalk, H., Generative modeling of turbulence, Phys. Fluids, 34, 3, Article 035114 pp., mar 2022 |
| [11] | Eling, C.; Oz, Y., The anomalous scaling exponents of turbulence in general dimension from random geometry, J. High Energy Phys., 2015, 1, 2015 · Zbl 1388.83431 |
| [12] | Frisch, U., Turbulence: The Legacy of A. N. Kolmogorov, 1995, Cambridge University Press · Zbl 0832.76001 |
| [13] | Fukami, K.; Fukagata, K.; Taira, K., Super-resolution reconstruction of turbulent flows with machine learning, J. Fluid Mech., 870, 106-120, 2019 |
| [14] | F. Heyder, J.P. Mellado, J. Schumacher, Generative convective parametrization of dry atmospheric boundary layer, 2023. |
| [15] | Ho, J.; Jain, A.; Abbeel, P., Denoising diffusion probabilistic models, Adv. Neural Inf. Process. Syst., 33, 6840-6851, 2020 |
| [16] | R. King, O. Hennigh, A. Mohan, M. Chertkov, From deep to physics-informed learning of turbulence: Diagnostics, 2018. |
| [17] | G. Kohl, L.-W. Chen, N. Thuerey, Turbulent flow simulation using autoregressive conditional diffusion models, 2023. |
| [18] | Kolmogorov, A. N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, C. R. Acad. Sci. URSS, 30, 301-305, 1941 · JFM 67.0850.06 |
| [19] | Kraichnan, R. H., Inertial ranges in two-dimensional turbulence, Phys. Fluids, 10, 7, 1417-1423, 1967 |
| [20] | Lellep, M.; Prexl, J.; Eckhardt, B.; Linkmann, M., Interpreted machine learning in fluid dynamics: explaining relaminarisation events in wall-bounded shear flows, J. Fluid Mech., 942, A2, 2022 · Zbl 1512.76089 |
| [21] | Li, B.; Yang, Z.; Zhang, X.; He, G.; Deng, B.-Q.; Shen, L., Using machine learning to detect the turbulent region in flow past a circular cylinder, J. Fluid Mech., 905, A10, 2020 · Zbl 1460.76389 |
| [22] | T. Li, L. Biferale, F. Bonaccorso, M.A. Scarpolini, M. Buzzicotti, Synthetic Lagrangian turbulence by generative diffusion models, 2023. |
| [23] | Li, T.; Buzzicotti, M.; Biferale, L.; Bonaccorso, F., Generative adversarial networks to infer velocity components in rotating turbulent flows, Eur. Phys. J. E, 46, 5, 31, May 2023 |
| [24] | M. Lienen, D. Lüdke, J. Hansen-Palmus, S. Günnemann, From zero to turbulence: Generative modeling for 3d flow simulation, 2023. |
| [25] | Loshchilov, I.; Hutter, F., Decoupled weight decay regularization, (International Conference on Learning Representations, 2019) |
| [26] | A.A. Moghaddam, A. Sadaghiyani, A deep learning framework for turbulence modeling using data assimilation and feature extraction, 2018. |
| [27] | A. Mohan, D. Daniel, M. Chertkov, D. Livescu, Compressed convolutional lstm: an efficient deep learning framework to model high fidelity 3d turbulence, 2019. |
| [28] | Oz, Y., Spontaneous symmetry breaking, conformal anomaly and incompressible fluid turbulence, J. High Energy Phys., 11, Article 040 pp., 2017 · Zbl 1383.81250 |
| [29] | Pandey, S.; Schumacher, J.; Sreenivasan, K. R., A perspective on machine learning in turbulent flows, J. Turbul., 21, 9-10, 567-584, 2020 |
| [30] | Rutgers, M. A., Forced 2d turbulence: experimental evidence of simultaneous inverse energy and forward enstrophy cascades, Phys. Rev. Lett., 81, 2244-2247, Sep 1998 |
| [31] | She, Z.-S.; Leveque, E., Universal scaling laws in fully developed turbulence, Phys. Rev. Lett., 72, 336-339, Jan 1994 |
| [32] | Shu, D.; Li, Z.; Farimani, A. B., A physics-informed diffusion model for high-fidelity flow field reconstruction, J. Comput. Phys., 478, Article 111972 pp., apr 2023 · Zbl 07660336 |
| [33] | D. Tretiak, A.T. Mohan, D. Livescu, Physics-constrained generative adversarial networks for 3d turbulence, 2022. |
| [34] | von Platen, P.; Patil, S.; Lozhkov, A.; Cuenca, P.; Lambert, N.; Rasul, K.; Davaadorj, M.; Wolf, T., Diffusers: state-of-the-art diffusion models, 2022 |
| [35] | Whittaker, T.; Janik, R. A.; Oz, Y., Neural network complexity of chaos and turbulence, Eur. Phys. J. E, 46, 7, 57, Jul 2023 |
| [36] | Yakhot, V., Mean-field approximation and a small parameter in turbulence theory, Phys. Rev. E, 63, Article 026307 pp., Jan 2001 |
| [37] | G. Yang, S. Sommer, A denoising diffusion model for fluid field prediction, 2023. |
| [38] | Yang, L.; Zhang, Z.; Song, Y.; Hong, S.; Xu, R.; Zhao, Y.; Zhang, W.; Cui, B.; Yang, M.-H., Diffusion models: a comprehensive survey of methods and applications, ACM Comput. Surv., sep 2023, Just Accepted |
| [39] | Zhou, Z.; Li, B.; Yang, X.; Yang, Z., A robust super-resolution reconstruction model of turbulent flow data based on deep learning, Comput. Fluids, 239, Article 105382 pp., 2022 · Zbl 1521.76271 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
