Noisy chaotic time series forecast approximated by combining Reny's entropy with energy associated to series method: Application to rainfall series

Rivero, Cristian Rodríguez; Pucheta, Juliàn; Laboret, Sergio; Sauchelli, Víctor; Orjuela-Cañón, Álvaro David; Franco, Leonardo

doi:10.1109/la-cci.2016.7885702

Cited by 1 publication

(2 citation statements)

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“…Chaotic time series prediction (CTSP) is involved in various domains of social and natural sciences, such as copper metal price, oilfield water injection, wind power, and rainfall [1]- [4]. Over the last decade, CTSP has been applied to the study of blood glucose, disease, and gait in humans [5]- [7].…”

Section: Introductionmentioning

confidence: 99%

“…Said Jadid et al developed an unscented Kalman filter and NARX neural network to analyze and predict the Lorenz time series [11]. Combined with the smoothing approach considering the entropic information, a noisy forecast method was applied to chaotic rainfall time series [4]. Nhabangue et al proposed a functional link extreme learning machine to CT SP [15], and Xu et al applied a hybrid regularized echo state network to forecast multivariate CTSP [16].…”

Section: Introductionmentioning

confidence: 99%

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Deep Hybrid Neural Network and Improved Differential Neuroevolution for Chaotic Time Series Prediction

Huang

Yuan

2020

IEEE Access

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Chaos is widespread in non-linear systems such as finance, energy, and weather. In the chaos system, a variable changing with time generates a chaotic time series, which contains a wealth of information about the non-linear system, and it is helpful for us to analyze and understand chaos systems. Traditional hybrid models for chaotic time series prediction based on neural networks have problems such as low prediction accuracy and difficulty in determining the network topologies. In recent years, the chaotic time series prediction has attached the attention of researchers in the area of deep learning. In this paper, we use a deep hybrid neural network (DHNN) based on convolutional neural network (CNN), gated recurrent unit (GRU) network, and attention mechanism to predict chaotic time series. Besides, we use the idea of neuroevolution to optimize the topologies of the DHNN. In the DHNN, we use CNN to capture spatial features from phase space reconstruction of chaotic time series. Then, we combine spatial features with the original chaotic time series. GRU extracts the spatio-temporal features from the combined sequence, and an attention mechanism with a non-linear activation function is designed to capture critical spatio-temporal features. Besides, we propose an improved differential evolution (IDE) algorithm to optimize the topologies of the DHNN, including the filter sizes of CNN and the number of hidden neurons of GRU. We develop the IDE with an adaptive mutation operator and dynamic chaos crossover operator, which can improve convergence speed and reduce optimization time. In this paper, we use the theoretical Lorenz datasets, monthly mean total sunspot datasets, and the actual coalmine gas concentration datasets to verify the prediction accuracy of the proposed prediction model. Experimental results have shown that the proposed prediction model performs well in chaotic time series forecasting. INDEX TERMS Chaotic time series prediction, convolutional neural network, gated recurrent unit, attention mechanism, improved differential evolution, neuroevolution

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