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

Doan, Nguyen Anh Khoa; Polifke, Wolfgang; Magri, Luca

doi:10.1098/rspa.2021.0135

Cited by 26 publications

(17 citation statements)

References 44 publications

(70 reference statements)

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“…For brevity, this model is referred to as "MFE". Because the MFE captures qualitatively nonlinear phenomena, such as relaminarization and turbulent bursts, it has been employed to qualitatively study turbulence transition [45,46] and predictability of chaotic flows [25,39]. The dynamics are governed by the non-dimensional Navier-Stokes equations for forced incompressible flows…”

Section: A Qualitative Model Of Chaotic Shear Flowmentioning

confidence: 99%

“…where k e = 0.1 is the user-defined extreme event's threshold [39]. Physically, an extreme event occurs because the stable laminar solution intermittently attracts the chaotic dynamics up to full laminarization.…”

Section: A Qualitative Model Of Chaotic Shear Flowmentioning

confidence: 99%

“…To assess how far in advance the networks predict extreme events, we use the prediction horizon for extreme events, PH ee . The prediction horizon is a metric to evaluate the timeaccurate prediction of chaotic dynamics with data-driven methods [33,35,36,39]. In this work, it is defined as the time interval during which the absolute error between the kinetic energy predicted by the ESN, k ESN , and the true kinetic energy, k True is bounded as…”

Section: B Prediction Horizon Of Extreme Eventsmentioning

confidence: 99%

“…Finally, we study the statistics of the flow variables, following Srinivasan et al [25] and Doan et al [39]. We assess the prediction for the generic variable α through the Normalized Root Mean Square Error (NRMSE) with respect to the true data,…”

Section: Statistical Prediction Of Extreme Eventsmentioning

confidence: 99%

“…To improve the performance of the networks, prior knowledge of the governing equations has been embedded in the hybrid [36] and physics-informed [37] architectures. In fluid dynamics, echo state networks have been employed to (i) learn [30] and (ii) optimize ergodic averages in thermoacoustic oscillations [38]; (iii) time-accurately [39] and (iv) statistically predict extreme events in chaotic flows [39,40]. In particular, Doan et al [39] studied the effect of including prior knowledge of the governing equations in a chaotic shear flow model to improve the prediction of extreme events when only a small training set is available.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Data-driven prediction and control of extreme events in a chaotic flow

Racca¹,

Magri²

2022

Preprint

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An extreme event is a sudden and violent change in the state of a nonlinear system. In fluid dynamics, extreme events can have adverse effects on the system's optimal design and operability, which calls for accurate methods for their prediction and control. In this paper, we propose a data-driven methodology for the prediction and control of extreme events in a chaotic shear flow.The approach is based on echo state networks, which are a type of reservoir computing that learn temporal correlations within a time-dependent dataset. The objective is five-fold. First, we exploit ad-hoc metrics from binary classification to analyse (i) how many of the extreme events predicted by the network actually occur in the test set (precision), and (ii) how many extreme events are missed by the network (recall). We apply a principled strategy for optimal hyperparameter selection, which is key to the networks' performance. Second, we focus on the time-accurate prediction of extreme events. We show that echo state networks are able to predict extreme events well beyond the predictability time, i.e., up to more than five Lyapunov times. Third, we focus on the longterm prediction of extreme events from a statistical point of view. By training the networks with datasets that contain non-converged statistics, we show that the networks are able to learn and extrapolate the flow's long-term statistics. In other words, the networks are able to extrapolate in time from relatively short time series. Fourth, we design a simple and effective control strategy to prevent extreme events from occurring. The control strategy decreases the occurrence of extreme events up to one order of magnitude with respect to the uncontrolled system. Finally, we analyse the robustness of the results for a range of Reynolds numbers. We show that the networks perform well across a wide range of regimes. This work opens up new possibilities for the data-driven prediction and control of extreme events in chaotic systems.

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Section: A Qualitative Model Of Chaotic Shear Flowmentioning

confidence: 99%

Section: A Qualitative Model Of Chaotic Shear Flowmentioning

confidence: 99%

Section: B Prediction Horizon Of Extreme Eventsmentioning

confidence: 99%

Section: Statistical Prediction Of Extreme Eventsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Data-driven prediction and control of extreme events in a chaotic flow

Racca¹,

Magri²

2022

Preprint

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Data-Driven Stability Analysis of a Chaotic Time-Delayed System

Margazoglou

Magri

2023

Computational Science – ICCS 2023

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Stability analysis of chaotic systems from data

Margazoglou

Magri

2023

Nonlinear Dyn

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The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability analysis, we linearize the equations of the dynamical system around a reference point and compute the properties of the tangent space (i.e. the Jacobian). The main goal of this paper is to propose a method that infers the Jacobian, thus, the stability properties, from observables (data). First, we propose the echo state network (ESN) with the Recycle validation as a tool to accurately infer the chaotic dynamics from data. Second, we mathematically derive the Jacobian of the echo state network, which provides the evolution of infinitesimal perturbations. Third, we analyse the stability properties of the Jacobian inferred from the ESN and compare them with the benchmark results obtained by linearizing the equations. The ESN correctly infers the nonlinear solution and its tangent space with negligible numerical errors. In detail, we compute from data only (i) the long-term statistics of the chaotic state; (ii) the covariant Lyapunov vectors; (iii) the Lyapunov spectrum; (iv) the finite-time Lyapunov exponents; (v) and the angles between the stable, neutral, and unstable splittings of the tangent space (the degree of hyperbolicity of the attractor). This work opens up new opportunities for the computation of stability properties of nonlinear systems from data, instead of equations.

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

Cited by 26 publications

References 44 publications

Data-driven prediction and control of extreme events in a chaotic flow

Data-driven prediction and control of extreme events in a chaotic flow

Data-Driven Stability Analysis of a Chaotic Time-Delayed System

Stability analysis of chaotic systems from data

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