WOA-Based Echo State Network for Chaotic Time Series Prediction

We present a new chaotic times prediction model inspired by the bubble-net predation of whales. The echo state network (ESN) is a new type of recurrent neural network. However, selecting parameters empirically for the ESN cannot guarantee the accuracy of the prediction. The whale optimization algorithm (WOA) imitates the bubble-net predation of whales and ensures the rapid convergence of selecting network parameters. A new prediction model, WOA-ESN, in which the WOA and the ESN are incorporated, is proposed in this paper. In addition, a simplified cross-validation (CV) method is proposed to take into account the approximation performance and generalization ability of the WOA-ESN. In experiments, the WOA-ESN is used for Mackey-Glass and Lorenz chaotic time series predictions, and the results are compared with the ESN based on particle swarm optimization (PSO-ESN), the ESN based on genetic algorithm (GA-ESN), and ESN. The results show that the proposed model has the best prediction performance.

[1]  Patrick R Hof,et al.  Structure of the cerebral cortex of the humpback whale, Megaptera novaeangliae (Cetacea, Mysticeti, Balaenopteridae) , 2007, Anatomical record.

[2]  Andrew Lewis,et al.  The Whale Optimization Algorithm , 2016, Adv. Eng. Softw..

[3]  Adel M. Alimi,et al.  PSO-based analysis of Echo State Network parameters for time series forecasting , 2017, Appl. Soft Comput..

[4]  Ying Liu,et al.  Prediction for noisy nonlinear time series by echo state network based on dual estimation , 2012, Neurocomputing.

[5]  Herbert Jaeger,et al.  Optimization and applications of echo state networks with leaky- integrator neurons , 2007, Neural Networks.

[6]  Srinivas Peeta,et al.  Multiple measures-based chaotic time series for traffic flow prediction based on Bayesian theory , 2016, Nonlinear Dynamics.

[7]  Yaochu Jin,et al.  Evolutionary multi-objective generation of recurrent neural network ensembles for time series prediction , 2014, Neurocomputing.

[8]  Lin Lin,et al.  Genetic algorithm optimized double-reservoir echo state network for multi-regime time series prediction , 2017, Neurocomputing.

[9]  Yaochu Jin,et al.  Modeling neural plasticity in echo state networks for classification and regression , 2016, Inf. Sci..

[10]  Jordan B. Pollack,et al.  Recursive Distributed Representations , 1990, Artif. Intell..

[11]  Benjamin Schrauwen,et al.  Reservoir Computing Trends , 2012, KI - Künstliche Intelligenz.

[12]  Peter Tiño,et al.  Minimum Complexity Echo State Network , 2011, IEEE Transactions on Neural Networks.

[13]  Zhang Jia-Shu,et al.  Predicting Hyper-Chaotic Time Series Using Adaptive Higher-Order Nonlinear Filter , 2001 .

[14]  Haigen Hu,et al.  Multistability of delayed complex-valued recurrent neural networks with discontinuous real-imaginary-type activation functions , 2015 .

[15]  Junyi Yu,et al.  Chaotic time series prediction: From one to another , 2009 .

[16]  James McNames,et al.  Local averaging optimization for chaotic time series prediction , 2002, Neurocomputing.

[17]  Wang Yanhong,et al.  A prediction method based on wavelet transform and multiple models fusion for chaotic time series , 2017 .

[18]  JaegerHerbert,et al.  2007 Special Issue , 2007 .

[19]  Les E. Atlas,et al.  Recurrent neural networks and robust time series prediction , 1994, IEEE Trans. Neural Networks.

[20]  Gholamali Heydari,et al.  Chaotic time series prediction via artificial neural square fuzzy inference system , 2016, Expert Syst. Appl..

[21]  Fernando José Von Zuben,et al.  An extended echo state network using Volterra filtering and principal component analysis , 2012, Neural Networks.

[22]  Kyongmin Yeo,et al.  Data-driven Reconstruction of Nonlinear Dynamics from Sparse Observation , 2019, J. Comput. Phys..

[23]  Moon Ho Lee,et al.  Quantum quasi-cyclic low-density parity-check error-correcting codes , 2009 .

[24]  Jian Huang,et al.  Echo state network based predictive control with particle swarm optimization for pneumatic muscle actuator , 2016, J. Frankl. Inst..

[25]  Danilo P. Mandic,et al.  Regular nonlinear response of the driven Duffing oscillator to chaotic time series , 2009 .

[26]  Chi-Keong Goh,et al.  Co-evolutionary multi-task learning with predictive recurrence for multi-step chaotic time series prediction , 2017, Neurocomputing.

[27]  Noah A. Smith,et al.  Proceedings of NIPS , 2010, NIPS 2010.

[28]  William A. Watkins,et al.  Aerial Observation of Feeding Behavior in Four Baleen Whales: Eubalaena glacialis, Balaenoptera borealis, Megaptera novaeangliae, and Balaenoptera physalus , 1979 .

[29]  Harald Haas,et al.  Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication , 2004, Science.

[30]  Junfei Qiao,et al.  Growing Echo-State Network With Multiple Subreservoirs , 2017, IEEE Transactions on Neural Networks and Learning Systems.