- Access by Xinjiang University
Complexity of extreme-event prediction in turbulent flows
Phys. Rev. Fluids 9, 104603 – Published 17 October, 2024
DOI: https://doi.org/10.1103/PhysRevFluids.9.104603
Abstract
Predicting extreme events in turbulent flows represents a challenge due to chaos or modeling uncertainty. This paper addresses a fundamental but unexplored limitation in extreme-event forecasting: the minimum computational cost of producing accurate forecasts. The information bottleneck method is applied to massive ensembles of Kolmogorov flow simulations to construct optimal predictive models of dissipation bursts. It is shown that, to maintain relative predictive skill, the minimum model complexity (size) and the cost of predictions increase exponentially with the forecast horizon. This limitation is connected to causal uncertainty, whereby the number of states from which an extreme event may emerge increases with the forecast horizon. It is argued that, to maintain accuracy, data-driven models need to encode theses states, increasing their size and the amount of data necessary for training.
Physics Subject Headings (PhySH)
Article Text
References (47)
- P. K. Yeung, X. M. Zhai, and K. R. Sreenivasan, Extreme events in computational turbulence, Proc. Natl. Acad. Sci. USA 112, 12633 (2015).
- L. Biferale, F. Bonaccorso, I. M. Mazzitelli, M. A. T. van Hinsberg, A. S. Lanotte, S. Musacchio, P. Perlekar, and F. Toschi, Coherent structures and extreme events in rotating multiphase turbulent flows, Phys. Rev. X 6, 041036 (2016).
- D. Buaria, A. Pumir, E. Bodenschatz, and P.-K. Yeung, Extreme velocity gradients in turbulent flows, New J. Phys. 21, 043004 (2019).
- M. Avila, D. Barkley, and B. Hof, Transition to turbulence in pipe flow, Annu. Rev. Fluid Mech. 55, 575 (2023).
- T. Woollings, D. Barriopedro, J. Methven, S.-W. Son, O. Martius, B. Harvey, J. Sillmann, A. R. Lupo, and S. Seneviratne, Blocking and its response to climate change, Curr. Clim. Change Rep. 4, 287 (2018).
- Y. Yuan and A. Lozano-Durán, Limits to extreme event forecasting in chaotic systems, Physica D (Amsterdam, Neth.) 467, 134246 (2024).
- D. Qi and A. J. Majda, Using machine learning to predict extreme events in complex systems, Proc. Natl. Acad. Sci. USA 117, 52 (2020).
- A. Asch, E. J. Brady, H. Gallardo, J. Hood, B. Chu, and M. Farazmand, Model-assisted deep learning of rare extreme events from partial observations, Chaos 32, 043112 (2022).
- M. Lellep, J. Prexl, M. Linkmann, and B. Eckhardt, Using machine learning to predict extreme events in the Hénon map, Chaos 30, 013113 (2020).
- V. Pyragas and K. Pyragas, Using reservoir computer to predict and prevent extreme events, Phys. Lett. A 384, 126591 (2020).
- N. A. K. Doan, W. Polifke, and L. Magri, Short-and long-term predictions of chaotic flows and extreme events: A physics-constrained reservoir computing approach, Proc. R. Soc. A 477, 20210135 (2021).
- A. Racca and L. Magri, Data-driven prediction and control of extreme events in a chaotic flow, Phys. Rev. Fluids 7, 104402 (2022).
- E. N. Lorenz, Atmospheric predictability as revealed by naturally occurring analogues, J. Atmos. Sci. 26, 636 (1969).
- D. A. Donzis and K. R. Sreenivasan, Short-term forecasts and scaling of intense events in turbulence, J. Fluid Mech. 647, 13 (2010).
- M. Farazmand and T. P. Sapsis, A variational approach to probing extreme events in turbulent dynamical systems, Sci. Adv. 3, e1701533 (2017).
- P. J. Blonigan, M. Farazmand, and T. P. Sapsis, Are extreme dissipation events predictable in turbulent fluid flows? Phys. Rev. Fluids 4, 044606 (2019).
- P. Debue, V. Valori, C. Cuvier, F. Daviaud, J.-M. Foucaut, J.-.P Laval, C. Wiertel, V. Padilla, and B. Dubrulle, Three-dimensional analysis of precursors to non-viscous dissipation in an experimental turbulent flow, J. Fluid Mech. 914, A9 (2021).
- G. Sugihara and R.-M. May, Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series, Nature (London) 344, 734 (1990).
- L. Delle Monache, F. A. Eckel, D. L. Rife, B. Nagarajan, and K. Searight, Probabilistic weather prediction with an analog ensemble, Mon. Weather Rev. 141, 3498 (2013).
- N. Tishby and N. Zaslavsky, Deep learning and the information bottleneck principle, in Proceedings of the 2015 IEEE Information Theory Workshop (ITW) (IEEE, New York, 2015), pp. 1–5.
- A. M. Saxe, Y. Bansal, J. Dapello, M. Advani, A. Kolchinsky, B. D. Tracey, and D. D. Cox, On the information bottleneck theory of deep learning, J. Stat. Mech. (2019) 124020.
- P. Grassberger, Toward a quantitative theory of self-generated complexity, Int. J. Theor. Phys. 25, 907 (1986).
- J. P. Crutchfield and K. Young, Inferring statistical complexity, Phys. Rev. Lett. 63, 105 (1989).
- M. Rivera and X.-L. Wu, External dissipation in driven two-dimensional turbulence, Phys. Rev. Lett. 85, 976 (2000).
- D. Lucas and R. Kerswell, Spatiotemporal dynamics in two-dimensional Kolmogorov flow over large domains, J. Fluid Mech. 750, 518 (2014).
- J. Page, M. P. Brenner, and Rich R. Kerswell, Revealing the state space of turbulence using machine learning, Phys. Rev. Fluids 6, 034402 (2021).
- A. Vela-Martín and M. Avila, Large-scale patterns set the predictability limit of extreme events in Kolmogorov flow, J. Fluid Mech. 986, A2 (2024).
- S. Still, W. Bialek, and L. Bottou, Geometric clustering using the information bottleneck method, in Advances in Neural Information Processing Systems 16 (MIT Press, Cambridge, MA, 2003).
- S. Still, J. P. Crutchfield, and C. J. Ellison, Optimal causal inference: Estimating stored information and approximating causal architecture, Chaos 20, 037111 (2010).
- C. E. Leith, Theoretical skill of Monte Carlo forecasts, Mon. Weather Rev. 102, 409 (1974).
- M. Leutbecher and T. N. Palmer, Ensemble forecasting, J. Comput. Phys. 227, 3515 (2008).
- E. N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci. 20, 130 (1963).
- T. N. Palmer, Predicting uncertainty in forecasts of weather and climate, Rep. Prog. Phys. 63, 71 (2000).
- T. DelSole, Predictability and information theory. Part I: Measures of predictability, J. Atmos. Sci. 61, 2425 (2004).
- R. Abramov, A. J. Majda, and R. Kleeman, Information theory and predictability for low-frequency variability, J. Atmos. Sci. 62, 65 (2005).
- R. Kleeman, Information theory and dynamical system predictability, Entropy 13, 612 (2011).
- D. Giannakis and A. J. Majda, Quantifying the predictive skill in long-range forecasting. Part I: Coarse-grained predictions in a simple ocean model, J. Clim. 25, 1793 (2012).
- G. Yalnz, B. Hof, and N. B. Budanur, Coarse graining the state space of a turbulent flow using periodic orbits, Phys. Rev. Lett. 126, 244502 (2021).
- D. Fernex, B. R. Noack, and R. Semaan, Cluster-based network modeling—from snapshots to complex dynamical systems, Sci. Adv. 7, eabf5006 (2021).
- D. Floryan and M. D. Graham, Data-driven discovery of intrinsic dynamics, Nat. Mach. Intell. 4, 1113 (2022).
- E. Farzamnik, A. Ianiro, S. Discetti, N. Deng, K. Oberleithner, B. R. Noack, and V. Guerrero, From snapshots to manifolds—a tale of shear flows, J. Fluid Mech. 955, A34 (2023).
- C. R. Shalizi and J. P. Crutchfield, Computational mechanics: Pattern and prediction, structure and simplicity, J. Stat. Phys. 104, 817 (2001).
- S. Lloyd and H. Pagels, Complexity as thermodynamic depth, Ann. Phys. 188, 186 (1988).
- M. A. Mohamad and T. P. Sapsis, Sequential sampling strategy for extreme event statistics in nonlinear dynamical systems, Proc. Natl. Acad. Sci. USA 115, 11138 (2018).
- J. Rolland, Collapse of transitional wall turbulence captured using a rare events algorithm, J. Fluid Mech. 931, A22 (2022).
- S. Gomé, L. S. Tuckerman, and D. Barkley, Extreme events in transitional turbulence, Philos. Trans. R. Soc. A 380, 20210036 (2022).
- V. Latora and M. Baranger, Kolmogorov-Sinai entropy rate versus physical entropy, Phys. Rev. Lett. 82, 520 (1999).
