scholarly journals Maximizing the Statistical Diversity of an Ensemble of Bred Vectors by Using the Geometric Norm

2011 ◽  
Vol 68 (7) ◽  
pp. 1507-1512 ◽  
Author(s):  
Diego Pazó ◽  
Miguel A. Rodríguez ◽  
Juan M. López
Keyword(s):  
Growth Rate ◽  
Chaotic Systems ◽  
Numerical Integrations ◽  
Spatially Extended ◽  
Bred Vectors ◽  
Lorenz 96 ◽  
Lyapunov Vector ◽  
Unstable Direction

Abstract It is shown that the choice of the norm has a great impact on the construction of ensembles of bred vectors. The geometric norm maximizes (in comparison with other norms such as the Euclidean one) the statistical diversity of the ensemble while at the same time it enhances the growth rate of the bred vector and its projection on the linearly most unstable direction (i.e., the Lyapunov vector). The geometric norm is also optimal in providing the least fluctuating ensemble dimension among all the spectrum of norms studied. The results are exemplified with numerical integrations of a toy model of the atmosphere (the Lorenz-96 model), but these findings are expected to be generic for spatially extended chaotic systems.

Dynamic scaling of bred vectors in spatially extended chaotic systems

2006 ◽  
Vol 76 (5) ◽  
pp. 767-773 ◽  
Author(s):  
C Primo ◽  
I. G Szendro ◽  
M. A Rodríguez ◽  
J. M López
Keyword(s):  
Chaotic Systems ◽  
Dynamic Scaling ◽  
Spatially Extended ◽  
Bred Vectors

Correlated Brownian motion and diffusion of defects in spatially extended chaotic systems

2019 ◽  
Vol 29 (7) ◽  
pp. 071104 ◽  
Author(s):  
S. T. da Silva ◽  
T. L. Prado ◽  
S. R. Lopes ◽  
R. L. Viana
Keyword(s):  
Brownian Motion ◽  
Chaotic Systems ◽  
Spatially Extended ◽  
And Diffusion

Particle Filters with Nudging in Multiscale Chaotic Systems: With Application to the Lorenz ’96 Atmospheric Model

2020 ◽  
Vol 30 (4) ◽  
pp. 1519-1552 ◽  
Author(s):  
Hoong C. Yeong ◽  
Ryne T. Beeson ◽  
N. Sri Namachchivaya ◽  
Nicolas Perkowski
Keyword(s):  
Chaotic Systems ◽  
Particle Filters ◽  
Atmospheric Model ◽  
Lorenz 96

scholarly journals ANOMALOUS SYNCHRONIZATION OF SPATIALLY EXTENDED CHAOTIC SYSTEMS IN THE PRESENCE OF ASYMMETRIC COUPLING

2005 ◽  
Vol 05 (02) ◽  
pp. L251-L258
Author(s):  
S. BOCCALETTI ◽  
C. MENDOZA ◽  
J. BRAGARD
Keyword(s):  
Chaotic Systems ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Turbulence Regime ◽  
Asymmetric Coupling ◽  
Spatially Extended ◽  
Ginzburg Landau Equations ◽  
Phase Singularities ◽  
Coupling Strengths ◽  
Spatially Extended Systems

This paper describes the effects of an asymmetric coupling in the synchronization of two spatially extended systems. Namely, we report the consequences induced by the presence of asymmetries in the coupling configuration of a pair of one-dimensional fields obeying Complex Ginzburg–Landau equations. While synchronization always occurs for large enough coupling strengths, asymmetries have the effect of enhancing synchronization and play a crucial role in setting the threshold for the appearance of the synchronized dynamics, as well as in selecting the statistical and dynamical properties of the synchronized motion. We discuss the process of synchronization in the presence of asymmetries by using some analytic expansions valid for a regime of soft spatial temporal chaos (i.e. phase turbulence regime). The influence of phase singularities that break the validity of the analysis is also discussed.

scholarly journals Predictors and predictands of linear response in spatially extended systems

2021 ◽  
Author(s):  
Umberto Maria Tomasini ◽  
Valerio Lucarini
Keyword(s):  
Complex System ◽  
Linear Response ◽  
Predictive Ability ◽  
Local Observable ◽  
Extended System ◽  
Unperturbed State ◽  
Spatially Extended ◽  
Statistical Mechanical ◽  
Spatially Extended Systems ◽  
Lorenz 96

AbstractThe goal of response theory, in each of its many statistical mechanical formulations, is to predict the perturbed response of a system from the knowledge of the unperturbed state and of the applied perturbation. A new recent angle on the problem focuses on providing a method to perform predictions of the change in one observable of the system using the change in a second observable as a surrogate for the actual forcing. Such a viewpoint tries to address the very relevant problem of causal links within complex system when only incomplete information is available. We present here a method for quantifying and ranking the predictive ability of observables and use it to investigate the response of a paradigmatic spatially extended system, the Lorenz ’96 model. We perturb locally the system and we then study to what extent a given local observable can predict the behaviour of a separate local observable. We show that this approach can reveal insights on the way a signal propagates inside the system. We also show that the procedure becomes more efficient if one considers multiple acting forcings and, correspondingly, multiple observables as predictors of the observable of interest.

scholarly journals Combining Ensemble Kalman Filter and Reservoir Computing to predict spatio-temporal chaotic systems from imperfect observations and models

2020 ◽  
Author(s):  
Futo Tomizawa ◽  
Yohei Sawada
Keyword(s):  
Machine Learning ◽  
Kalman Filter ◽  
Chaotic Systems ◽  
Weather Prediction ◽  
Machine Learning Techniques ◽  
Reservoir Computing ◽  
Learning Techniques ◽  
Spatio Temporal ◽  
Ensemble Transform Kalman Filter ◽  
Lorenz 96

Abstract. Prediction of spatio-temporal chaotic systems is important in various fields, such as Numerical Weather Prediction (NWP). While data assimilation methods have been applied in NWP, machine learning techniques, such as Reservoir Computing (RC), are recently recognized as promising tools to predict spatio-temporal chaotic systems. However, the sensitivity of the skill of the machine learning based prediction to the imperfectness of observations is unclear. In this study, we evaluate the skill of RC with noisy and sparsely distributed observations. We intensively compare the performances of RC and Local Ensemble Transform Kalman Filter (LETKF) by applying them to the prediction of the Lorenz 96 system. Although RC can successfully predict the Lorenz 96 system if the system is perfectly observed, we find that RC is vulnerable to observation sparsity compared with LETKF. To overcome this limitation of RC, we propose to combine LETKF and RC. In our proposed method, the system is predicted by RC that learned the analysis time series estimated by LETKF. Our proposed method can successfully predict the Lorenz 96 system using noisy and sparsely distributed observations. Most importantly, our method can predict better than LETKF when the process-based model is imperfect.

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