Chaotic Time Series Prediction Research Articles

Grain storage temperature prediction based on chaos and enhanced RBF neural network

Grain storage has very strict temperature requirements. Aiming at the problems of nonlinear characteristics and poor prediction accuracy of temperature parameters in grain storage, a combination of chaos theory and enhanced radial basis neural network is proposed as a temperature prediction model for grain storage (C-ERBF). The model first determines the embedding dimension and time delay of the grain storage temperature sequence using chaos theory. It then calculates the Lyapunov exponent to confirm its chaotic properties and reconstructs the sequence in the phase space to extract the hidden dynamic information and structure behind the sequence. Furthermore, the q-Normalized Least Mean Square Fourth (qXE-NLMF) algorithm is designed to enhance the radial basis function (RBF) neural network model for weight updating, to improve its prediction accuracy, and to accelerate the training speed of the model. As verified by the simulation experiments of Mackey–Glass chaotic time series prediction, the enhanced RBF (ERBF) network has faster convergence speed and lower steady-state error compared to the traditional RBF network. Finally, the optimized dataset from chaos theory is input into the model to achieve accurate predictions of grain storage temperature series. The experimental results show that the proposed C-ERBF model has higher prediction accuracy compared to other time series prediction methods. It can realize the grain pile temperature in advance, and take control measures in advance. This proactive approach significantly reduces the consumption of stored grain and prevents issues before they arise.

A chaotic time series prediction model based on the improved dung beetle optimizer and echo state network

Echo state network (ESN) possesses advantages such as simple network structure, ease of training, and reliable prediction performance, making them widely applied in the field of time series prediction. Selecting the optimal reservoir parameters is a key issue in ESN research, as it determines the effectiveness of the network prediction, and it is crucial to design an efficient optimization method for parameter optimization. This paper introduces an improved version of the dung beetle optimizer (IDBO), which employs various strategies to enhance population initialization, algorithm optimization capability, and convergence speed. For theoretical function optimization problems, comparing IDBO with other commonly used optimization methods validated its effectiveness and feasibility. Subsequently, combining IDBO with ESN to construct a new model, IDBO-ESN, and conducting time series prediction experiments, the superior performance of this model is verified on two benchmark datasets and one real dataset.

High- accuracy chaotic time series prediction of the flexible beam-ring model based on P$$\_$$CNN-BiLSTM ED network

High- accuracy chaotic time series prediction of the flexible beam-ring model based on P$$\_$$CNN-BiLSTM ED network

Chaotic laser time series prediction based on an improved logistic mapping algorithm echo state network

Chaos synchronization plays vital functions in the fields of optical chaos secure communication. The synchronization performance can be significantly degraded by parameter mismatches between the chaotic transmitter and receiver. In this paper, the Deep-Logistical Mapping Echo State Network (D-LMESN) is proposed to enhance the performance of chaos synchronization. The network is upgraded by using an improved logical mapping algorithm and a deep reserve pool structure with phase space reconstruction. Results show that D-LMESN exhibits better performance in the prediction of chaotic time series, thanks to the adaptive parameter adjustment, which increases the ability to capture the dynamic characteristics of complex systems. Compared with ESN, the mean square error of this model is reduced by 55% and 72%, respectively, in chaotic laser simulation and actual data experiments. This provides a new possibility, to our knowledge, for the development of chaotic secure communication.

Multi-Step-Ahead Prediction of Chaotic Time Series: Self-Healing Algorithm for Restoring Values at Non-Predictable Points

Multi-Step-Ahead Prediction of Chaotic Time Series: Self-Healing Algorithm for Restoring Values at Non-Predictable Points

Sparse compressed deep echo state network with improved arithmetic optimization algorithm for chaotic time series prediction

A sparse compressed deep echo state network (SCDESN) incorporating sparse input units, compressed sampling and principal component analysis (PCA) units is proposed in this paper, and theoretically proved the sufficient and necessary conditions to ensure the echo state characteristics of the proposed scheme. In addition, a hybrid arithmetic optimization algorithm based on matrix design strategy and boundary selection strategy (SVD-HAOA) was proposed to optimize the hyper-parameters of the SCDESN model, taking into account the characteristics of the SCDESN model. The steps and process for optimizing the hyper parameters of the SCDESN model using SVD-HAOA were presented. Finally, the SCDESN model optimized by SVD-HAOA was experimentally and summarized on a classic benchmark dataset and two real-world chaotic time series. The outcomes of the simulation indicated that the suggested model surpassed alternative models in performance and enhanced computational efficiency while maintaining prediction accuracy. This model may serve as a viable alternative for real-world applications. Noteworthy, the source code of SCDESN-SVD-HAOA is publicly available at https://github.com/qiuqiuyaaa/SCDESN-SVD-HAOA.

Enhancing short-term chaotic wind speed time-series prediction using hybrid approach with multiple data sets

Enhancing short-term chaotic wind speed time-series prediction using hybrid approach with multiple data sets

Chaotic time series prediction based on physics-informed neural operator

This paper investigates the prediction of chaotic time series using physics-informed neural operator (PINO) with different driven methods, such as data-driven method, physics-driven method, and hybrid data-physics-driven method. Here, the chaotic time series are generated from two classical time delayed chaotic systems, including Mackey–Glass equation (MG) and Optoelectronic Oscillator (OEO). The simulation results from these two chaotic systems or experimental results from Optoelectronic Oscillator demonstrate that when there is enough data with good quality, it is possible to train the model solely using data-driven method. Conversely, when possessing complete mastery of the physical prior knowledge, it is also available to train the model solely using physics-driven method, indicating there is no need to prepare label datasets as in data-driven method. However, when dataset quality is poor, for example, contaminated by noise, and precise physical prior knowledge is not fully acquired, the hybrid method will have a better performance.

Prediction of Multivariate Chaotic Time Series using GRU, LSTM and RNN

Prediction of Multivariate Chaotic Time Series using GRU, LSTM and RNN

BLSTM convolution and self-attention network enabled recursive and direct prediction for optical chaos.

Chaotic time series prediction has attracted much attention in recent years because of its important applications, such as security analysis for random number generators and chaos synchronization in private communications. Herein, we propose a BLSTM convolution and self-attention network model to predict the optical chaos. We validate the model's capability for direct and recursive prediction, and the model dramatically reduces the accumulation of errors. Moreover, the time duration prediction of optical chaos is increased with comparative accuracy where the predicted sequence length reaches 4 ns with normalized mean squared error (NMSE) of less than 0.01.

A chaotic time series combined prediction model for improving trend lagging

AbstractChaotic time series prediction is a prediction method based on chaos theory, and has important theoretical and application value. At present, most prediction methods only pursue digital fitting and do not consider the directional trend. In addition, using the single model will not achieve better prediction results. Therefore, a chaotic time series combined prediction model for improving trend lagging (ITL) is proposed. An improved dual‐stage attention‐based long short‐term memory model with the improved training objective fuction is designed to solve the trend lagging problem. Then, an auto regressive moving average model with the sliding window is established to mine other characteristics of the time series except nonlinear characteristic. Finally, the idea of optimization algorithm is introduced to construct a time series combined prediction model with high accuracy based on the above two models, so as to perform the chaotic time series prediction from multiple perspectives. Multiple datasets are selected as experimental datasets, and the proposed method is compared with common prediction methods. The results show that the proposed method can achieve single‐step prediction with high accuracy and effectively improve the lagging of chaotic time series prediction. This research can provide theoretical support for the complex chaotic time series prediction.

Experimental Demonstration of Reservoir Computing with Self-Assembled Percolating Networks of Nanoparticles.

The complex self-assembled network of neurons and synapses that comprises the biological brain enables natural information processing with remarkable efficiency. Percolating networks of nanoparticles (PNNs) are complex self-assembled nanoscale systems that have been shown to possess many promising brain-like attributes and which are therefore appealing systems for neuromorphic computation. Here experiments are performed that show that PNNs can be utilized as physical reservoirs within a nanoelectronic reservoir computing framework and demonstrate successful computation for several benchmark tasks (chaotic time series prediction, nonlinear transformation, and memory capacity). For each task, relevant literature results are compiled and it is shown that the performance of the PNNs compares favorably to that previously reported from nanoelectronic reservoirs. It is then demonstrated experimentally that PNNs can be used for spoken digit recognition with state-of-the-art accuracy. Finally, a parallel reservoir architecture is emulated, which increases the dimensionality and richness of the reservoir outputs and results in further improvements in performance across all tasks.

Benchmarking reservoir computing for residential energy demand forecasting

In the energy sector, accurate demand forecasts are vital but often limited by the available computational power. Reservoir computing (RC) or echo-state networks excel in chaotic time series prediction, with lower computational requirements compared to other recurrent network based methods like LSTMs. Next-generation reservoir computing (NG-RC) is a newer, more efficient variant of classical RC originating from nonlinear vector autoregression and therefore missing the randomness of classical RC. In our study, we evaluate RC and NG-RC for day-ahead energy demand predictions on four data sets and compare it to LSTMs and a naive persistence approach. We find that NG-RC outperforms all other methods when considering the root mean squared error on all data sets but struggles with very small or zero demands. Additionally, it offers a very computationally effective hyperparameter optimization and excels in replicating the inherent volatility and the erratic behavior of energy demands.

CNN-LSTM based incremental attention mechanism enabled phase-space reconstruction for chaotic time series prediction

To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network, we propose a convolutional neural network (CNN)-long short-term memory (LSTM) prediction model based on the incremental attention mechanism. Firstly, a traversal search is conducted through the traversal layer for finite parameters in the phase space. Then, an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria (DWC). The phase space parameters that best meet DWC are selected and fed into the input layer. Finally, the constructed CNN-LSTM network extracts spatiotemporal features and provides the final prediction results. The model is verified using Logistic, Lorenz, and sunspot chaotic time series, and the performance is compared from the two dimensions of prediction accuracy and network phase space structure. Additionally, the CNN-LSTM network based on incremental attention is compared with LSTM, CNN, recurrent neural network (RNN), and support vector regression (SVR) for prediction accuracy. The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy. Also, the algorithm to estimate the phase space parameter is compared with the traditional CAO, false nearest neighbor, and C–C, three typical methods for determining the chaotic phase space parameters. The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks, including CNN-LSTM, LSTM, CNN, RNN, and SVR.

Photonic implementation of the input and reservoir layers for a reservoir computing system based on a single VCSEL with two Mach-Zehnder modulators

Hardware implementation of reservoir computing (RC), which could reduce the power consumption of machine learning and significantly enhance data processing speed, holds the potential to develop the next generation of machine learning hardware devices and chips. Due to the existing solution only implementing reservoir layers, the information processing speed of photonics RC system are limited. In this paper, a photonic implementation of a VMM-RC system based on single Vertical Cavity Surface Emitting Laser (VCSEL) with two Mach Zehnder modulators (MZMs) has been proposed. Unlike previous work, both the input and reservoir layers are realized in the optical domain. Additionally, the impact of various mask signals, such as Two-level mask, Six-level mask, and chaos mask signal, employed in system, has been investigated. The system's performance improves with the use of more complex mask(t). The minimum Normalized mean square error (NMSE) can reach 0.0020 (0.0456) for Santa-Fe chaotic time series prediction in simulation (experiment), while the minimum Word Error Rate (WER) can 0.0677 for handwritten digits recognition numerically. The VMM-RC proposed is instrumental in advancing the development of photonic RC by overcoming the long-standing limitations of photonic RC systems in reservoir implementation. Linear matrix computing units (the input layer) and nonlinear computing units (the reservoir layer) are simultaneously implemented in the optical domain, significantly enhancing the information processing speed of photonic RC systems.

A Modified Sine Cosine Algorithm for Numerical Optimization

Sine cosine algorithm (SCA) is a recently developed meta-heuristic method based on the characteristics of sine and cosine functions. However, SCA algorithm may suffer premature convergence in solving complex optimization problems. To mitigate this limitation, a modified SCA (MSCA) is developed to achieve an effective balance between exploration and exploitation. Specifically, the conversion parameter can be configured adaptively by using the individual fitness information in the evolution process to guide the individual search behavior. After that, an inertia weight is embedded in the position updating equation to further improve the search accuracy and accelerate the convergence speed. The performance of MSCA algorithm is investigated on 13 benchmark functions and the chaotic time series prediction problem. Experimental results demonstrate that MSCA algorithm is more effective than the other optimization methods.

Reservoir computing system based on mutually delay-coupled semiconductor lasers with optical feedback

Reservoir Computing (RC), an evolution from Recurrent Neural Networks (RNN), not only represents a unique machine learning paradigm, but also serves as a neuromorphic framework that mirrors the intricate cortical circuits of the human brain. This paper proposes another new photonic RC system based on four basic photonic reservoir computing architectures (single photonic RC system, the parallel photonic RC system, the dual-feedback loop-based photonic RC system and the mutually coupled photonic RC system). System proposed uses optical injection for signal input and retains two parallel responsive semiconductor lasers (R-SLs) with self-feedback loops. Meanwhile, two relatively independent R-SLs are mutually coupled via two coupling lines. The new photonic RC system adds only two sections of fiber compared to the parallel photonic RC system and the mutually coupled photonic RC system. The experiments show that the system proposed has significant advantages on the nonlinear auto regressive moving average series tasks, the chaotic time series prediction tasks and the waveform classification task. More importantly, the memory capacity of system proposed can be adjust by controlling the delay time of the self-feedback loops, so it has higher memory capacity to handle the higher order nonlinear auto regressive moving average tasks (NARMA20 and NARMA30) after optimizing the parameters.

Dynamic adaptive graph convolutional transformer with broad learning system for multi-dimensional chaotic time series prediction

Chaotic time series data is extensively applied in financial stocks, climate monitoring, and sea clutter, in which data fusion from various sources and multi-sensor information make accurate predictions of chaotic time series challenging under complex nonlinear conditions. Previous works focus on designing different model frameworks to capture the temporal dependence and extract richer nonlinear features to improve the accuracy of univariate chaotic time series prediction, which ignores the spatial dependence of multivariable. However, in this paper, we argue that spatial correlation among multiple variables is essential to improve the prediction accuracy of chaotic time series. To fill the gap, we innovatively propose a Dynamic Adaptive Graph Convolutional Transformer with a Broad Learning System (DAGCT-BLS), a GCN and Transformer-based model utilizing multivariate spatial dependence for multi-dimensional chaotic time series forecasting. In DAGCT-BLS, the multivariate chaotic time series are reconstructed into the phase space, and the reconstructed data are rapidly feature-extracted using a cascade network BLS with frozen weights to maximize the retention of chaotic properties and nonlinear relationships. Then, the Dynamic Adaptive Graph Convolutional Network (DAGCN) is proposed to capture the spatial correlation among the multiple variables. Finally, improved multi-head attention of the Transformer Encoder is used to capture the temporal dependence of the phase point sequence. Experiments of our proposed model on three datasets (Lorenz, Rossler, and Sea clutter) show that DAGCT-BLS can achieve the best prediction performance and have strong interpretability, and multivariate-based joint modeling of chaotic time series helps to improve the prediction performance.

Short-term prediction for chaotic time series based on photonic reservoir computing using VCSEL with feedback loop

Short-term prediction for chaotic time series based on photonic reservoir computing using VCSEL with feedback loop

Hybrid parallel photonic reservoir computing with accelerated data processing speed

Reservoir computing is a bio-inspired approach especially suited for processing time-dependent information. In this work, we propose a hybrid reservoir computing scheme based on parallel photonic time-delay reservoirs with optical injection. The state of virtual nodes are evaluated from the combination of temporal outputs of parallel lasers. It is demonstrated that our proposed hybrid scheme enables photonic reservoir computer with shortened time interval θ and less virtual nodes number N, which could break through the limitation of short external cavity length in miniaturization of reservoir computing with photonic integrated circuits. The computational efficiency of photonic reservoir is numerically evaluated by chaotic time-series prediction task and memory capacity test. State-of-the-art speed performances reach 20 GSa/s with prediction error rate below 0.01. Our scheme bridges the areas of photonic integrated circuits and photonic information processing.