New Results for Prediction of Chaotic Systems Using Deep Recurrent Neural Networks

Serrano-Pérez, José de Jesús; Fernández‐Anaya, Guillermo; Carrillo-Moreno, S.; Yu, Wen

doi:10.1007/s11063-021-10466-1

Cited by 20 publications

(6 citation statements)

References 44 publications

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“…Their chaotic properties come from the fact that they are very sensitive to their initial conditions, which smallest changes completely modify the respective trajectories. They are also well known to show aperiodic behaviour which is apparently random and unpredictable [1,13].…”

Section: Methodsmentioning

confidence: 99%

Improving the Predictive Power of Historical Consistent Neural Networks

Rockefeller

Bah

Marivate

et al. 2022

The 8th International Conference on Time Series and Forecasting

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Section: Methodsmentioning

confidence: 99%

Improving the Predictive Power of Historical Consistent Neural Networks

Rockefeller

Bah

Marivate

et al. 2022

The 8th International Conference on Time Series and Forecasting

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“…The authors of [184] developed a FFNN-based prediction model to estimate the change in future state values of a Rössler system. In [169], the authors presented a gate recurrent unit-based Deep RNN model to forecast time series of three chaotic systems, (i) Lorenz, (ii) Rabinovich-Fabrikant, and (iii) Rössler, which showed better performance than the LSTM-based Deep RNN model. This model can also be used for real-time applications to predict the hyperturbulent frameworks to control the turbulence or synchronize the framework model.…”

Section: Input Layer ∈ Rmentioning

confidence: 99%

Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review

Ramadevi

Bingi

2022

Symmetry

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Traditional statistical, physical, and correlation models for chaotic time series prediction have problems, such as low forecasting accuracy, computational time, and difficulty determining the neural network’s topologies. Over a decade, various researchers have been working with these issues; however, it remains a challenge. Therefore, this review paper presents a comprehensive review of significant research conducted on various approaches for chaotic time series forecasting, using machine learning techniques such as convolutional neural network (CNN), wavelet neural network (WNN), fuzzy neural network (FNN), and long short-term memory (LSTM) in the nonlinear systems aforementioned above. The paper also aims to provide issues of individual forecasting approaches for better understanding and up-to-date knowledge for chaotic time series forecasting. The comprehensive review table summarizes the works closely associated with the mentioned issues. It includes published year, research country, forecasting approach, application, forecasting parameters, performance measures, and collected data area in this sector. Future improvements and current studies in this field are broadly examined. In addition, possible future scopes and limitations are closely discussed.

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“…In addition, an improvement, on the previously mentioned paper, in the prediction horizon and a reduction in the number of neurons used was reported in [12]. Finally, in [13], the authors used Recurrent Neural Networks (RNN) and Deep Recurrent Neural Networks (DRNN) to estimate the states of chaotic systems with optimal results, in terms of loss and accuracy.…”

Section: Introductionmentioning

confidence: 99%

A Recurrent Neural Network for Identifying Multiple Chaotic Systems

Echenausía-Monroy,

Pena Ramirez,

Álvarez

et al. 2024

Mathematics

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This paper presents a First-Order Recurrent Neural Network activated by a wavelet function, in particular a Morlet wavelet, with a fixed set of parameters and capable of identifying multiple chaotic systems. By maintaining a fixed structure for the neural network and using the same activation function, the network can successfully identify the three state variables of several different chaotic systems, including the Chua, PWL-Rössler, Anishchenko–Astakhov, Álvarez-Curiel, Aizawa, and Rucklidge models. The performance of this approach was validated by numerical simulations in which the accuracy of the state estimation was evaluated using the Mean Square Error (MSE) and the coefficient of determination (r2), which indicates how well the neural network identifies the behavior of the individual oscillators. In contrast to the methods found in the literature, where a neural network is optimized to identify a single system and its application to another model requires recalibration of the neural algorithm parameters, the proposed model uses a fixed set of parameters to efficiently identify seven chaotic systems. These results build on previously published work by the authors and advance the development of robust and generic neural network structures for the identification of multiple chaotic oscillators.

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New Results for Prediction of Chaotic Systems Using Deep Recurrent Neural Networks

Cited by 20 publications

References 44 publications

Improving the Predictive Power of Historical Consistent Neural Networks

Improving the Predictive Power of Historical Consistent Neural Networks

Chaotic Time Series Forecasting Approaches Using Machine Learning Techniques: A Review

A Recurrent Neural Network for Identifying Multiple Chaotic Systems

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