Geometry of the edge of chaos in a low-dimensional turbulent shear flow model

Joglekar, Madhura R.; Feudel, Ulrike; Yorke, James A.

doi:10.1103/physreve.91.052903

Cited by 12 publications

(23 citation statements)

References 51 publications

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“…The electronic supplementary material reports the expressions for v i and the equations for a i [36]. Detailed analysis of the MFE model was performed by Kim & Moehlis [39] and Joglekar et al [40].…”

Section: Extreme Events In a Model Of Chaotic Flowmentioning

confidence: 99%

Short- and long-term predictions of chaotic flows and extreme events: a physics-constrained reservoir computing approach

2021

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We propose a physics-constrained machine learning method—based on reservoir computing—to time-accurately predict extreme events and long-term velocity statistics in a model of chaotic flow. The method leverages the strengths of two different approaches: empirical modelling based on reservoir computing, which learns the chaotic dynamics from data only, and physical modelling based on conservation laws. This enables the reservoir computing framework to output physical predictions when training data are unavailable. We show that the combination of the two approaches is able to accurately reproduce the velocity statistics, and to predict the occurrence and amplitude of extreme events in a model of self-sustaining process in turbulence. In this flow, the extreme events are abrupt transitions from turbulent to quasi-laminar states, which are deterministic phenomena that cannot be traditionally predicted because of chaos. Furthermore, the physics-constrained machine learning method is shown to be robust with respect to noise. This work opens up new possibilities for synergistically enhancing data-driven methods with physical knowledge for the time-accurate prediction of chaotic flows.

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Section: Extreme Events In a Model Of Chaotic Flowmentioning

confidence: 99%

Short- and long-term predictions of chaotic flows and extreme events: a physics-constrained reservoir computing approach

2021

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“…The supplementary material reports the expressions for v i and the equations for a i [28]. Detailed analysis of the MFE model has been performed by Kim and Moehlis [31] and Joglekar et al [32].…”

Section: Extreme Events In a Model Of Shear Turbulencementioning

confidence: 99%

Short- and long-term prediction of a chaotic flow: A physics-constrained reservoir computing approach

Doan,

Polifke,

Magri

2021

Preprint

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We propose a physics-constrained machine learning method-based on reservoir computing-to time-accurately predict extreme events and long-term velocity statistics in a model of turbulent shear flow. The method leverages the strengths of two different approaches: empirical modelling based on reservoir computing, which learns the chaotic dynamics from data only, and physical modelling based on conservation laws, which extrapolates the dynamics when training data becomes unavailable. We show that the combination of the two approaches is able to accurately reproduce the velocity statistics and to predict the occurrence and amplitude of extreme events in a model of self-sustaining process in turbulence. In this flow, the extreme events are abrupt transitions from turbulent to quasi-laminar states, which are deterministic phenomena that cannot be traditionally predicted because of chaos. Furthermore, the physics-constrained machine learning method is shown to be robust with respect to noise. This work opens up new possibilities for synergistically enhancing data-driven methods with physical knowledge for the time-accurate prediction of chaotic flows.

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“…Reynolds number and the permissible perturbation amplitude for a given flow without the full computational burden of the NS equations [5,7,18,19,[42][43][44][45][46][47]. These models are constructed to capture the transitional behavior of wall-bounded shear flows.…”

Section: Low Dimensional Shear Flow Models Have Been Used To Provide ...mentioning

confidence: 99%

An input-output inspired method for permissible perturbation amplitude of transitional wall-bounded shear flows

Liu,

Gayme

2020

Preprint

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The precise set of parameters governing transition to turbulence in wall-bounded shear flows remains an open question; many theoretical bounds have been obtained, but there is not yet a consensus between these bounds and experimental/simulation results. In this work, we focus on a method to provide a provable Reynolds number dependent bound on the amplitude of perturbations a flow can sustain while maintaining the laminar state. Our analysis relies on an input-output approach that partitions the dynamics into a feedback interconnection of the linear and nonlinear dynamics (i.e., a Luré system that represents the nonlinearity as static feedback). We then construct quadratic constraints of the nonlinear term that is restricted by system physics to be energy conserving (lossless) and to have bounded input-output energy. Computing the region of attraction of the laminar state (set of safe perturbations) and permissible perturbation amplitude are then reformulated as Linear Matrix Inequalities (LMI), which provides a more computationally efficient solution than prevailing nonlinear approaches based on sum of squares programming.The proposed framework can also be used for energy method computations and linear stability analysis. We apply our approach to low dimensional nonlinear shear flow models for a range of Reynolds numbers. The results from our analytically derived bounds are consistent with the bounds identified through exhaustive simulations. However, they have the added benefit of being achieved at much lower computational cost and providing a provable guarantee that a certain level of perturbation is permissible.

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Geometry of the edge of chaos in a low-dimensional turbulent shear flow model

Cited by 12 publications

References 51 publications

Short- and long-term predictions of chaotic flows and extreme events: a physics-constrained reservoir computing approach

Short- and long-term predictions of chaotic flows and extreme events: a physics-constrained reservoir computing approach

Short- and long-term prediction of a chaotic flow: A physics-constrained reservoir computing approach

An input-output inspired method for permissible perturbation amplitude of transitional wall-bounded shear flows

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