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2012. The traditional Metropolis algorithm, when applied do the Ising models close to their critical points, suffers from severe critical slowing down problems. On the other hand, the GWO_ESN model exhibited good prediction performances in all five cases, indicating strong generalization capability of this model. The authors have no competing interests to declare. Besides, performances of the proposed model for prediction of data distributions in other cases need to be verified. The red points correspond to reflections sampled uniformly, whereas the green points represent reflections sampled as described in Sec. DOI: https://doi.org/10.1016/j.ijleo.2017.01.073. This is due to its single-site updating procedure, which is good for updating the short-wavelength components of the configurations, but very bad at updating the long-wavelength components. \usepackage[Euler]{upgreek} For comparison, the results of Υp are also shown with open symbols. Open symbols represent results for Υp. The network needs to calculate the error gradient in the training process. Wolff algorithm . The Grey Wolf Optimizer (GWO) is a novel swarm intelligence algorithm proposed by Mirjalili in 2014 (Saremi et al. 2017). Conditions and any applicable \oddsidemargin -1.0in The prediction results by these five models over the five time series data sets were compared with practical results and to each other in the way of fitting graphs. The MSE as an evaluation parameter in this study is defined as: where y^M22 Step2: Initialize parameters in ESN and Grey Wolf algorithm. 2015) (Han and Mu 2011). Additionally, experiments demonstrated significant enhancements of prediction accuracy of the proposed prediction method over different time series data sets. 2017). , the location of the ith wolf is defined as Xi=XI1,  XI2,  ⋯,  XIdM4 2015), and the proposed GWO_ESN model were involved in this prediction experiment. Huang et al. In: International Joint Conference on Neural Networks. It can be seen from the table that the GWO_ESN predictive model has relatively few running times under seven different datasets, although in some datasets the model running time is not dominant compared to the BP, Elman, and ESN prediction models, but it can be seen from Table 2 that, in the case of ensuring higher prediction accuracy, the model has a relatively small running time compared to other optimization models. The prediction model optimizes the echo state network, improves the accuracy of time series prediction, and shortens the prediction time to some extent. For comparison, results with the Wolff algorithm are also shown (filled symbols); (a) energy E for N=4×4×320 and (b) helicity modulus Υp for N=4×4×160 (circles), 4×4×320 (diamonds), and 4×4×480 (squares). Plos One, 12(3): 1–23. \usepackage[Euler]{upgreek} Moreover, performances of the BP neural network model and the Elman network model are unstable and their prediction performances may surpass the ESN model and the PSO-ESN model in certain cases, but never the GWO-ESN prediction model. In general, an ESN network can have a stable echo state attribute when 0 < SR <1. Neurocomputing, 159(1): 58–66. In other words, the GWO_ESN model is applicable for predictions of various time series data. Disqus. As a result, the accuracies of conventional ESN predictions are limited. Chandra, R. 2015. Therefore, α, β, and δ are the three optimal solutions currently and their updated locations are as follows: where Xα, Xβ, and Xδ are current locations of α, β, and δ, respectively; X(t) is the target location of grey wolf; Dα, Dβ, and Dδ are distances from the prey to α, β, and δ, respectively; X(t + 1) refers to the location vector with updated searching factor; C and A are random vectors. Instead, a single cluster is built. IEEE Latin America Transactions, 15(1): 145–153. Figure, If the maximized iteration number is not achieved, go back to Step b and repeat the process; if the maximized iteration number is achieved, obtain updated locations of α, β, δ and calculate the ultimate optimization result (W. Step1: Pre-process the original sequence and obtain de-noising and dimensionality reduced normalized data. Ren et al. 2018). The helicity modulus of the quasi-one-dimensional classical XY model is examined in connection with liquid He confined in nanopores. (a) N=4×4×Lz with Lz=80 (circles) and 480 (squares). Agreement. The idea comes from the construction of the probability q in both of the above-mentioned algorithms. Temperature Tb where the energy barrier ΔE′(1/2) vanishes as a function of 1/Leff for systems of different size: Lx=Ly=4 (filled circles), 6 (open squares), and 8 (open circles). {X_I}^d Energy of states with phase winding number i, ΔE(i)=Ei−E0; (a) N=4×4×160 and T/Tc=0.4, 0.6, and 0.7. A hybrid wavelet kernel SVM-based method using artificial bee colony algorithm for predicting the cyanotoxin content from experimental cyanobacteria concentrations in the Trasona reservoir (Northern Spain). \begin{document} DOI: https://doi.org/10.24963/ijcai.2017/366, Ren, T, Liu, S, Yan, G and Mu, HJ. and XIdM5 (b) T/Tc=0.6 and N=6×6×180, 4×4×160, and 4×4×480. 2018. \usepackage[mathscr]{eucal} 2017), and the ESN model (Li et al. Xiao, Q, Chu, C, Zhao, L. 2017. The specific updating equations are Eq (9), (10), (11), (12), (13), and (14). The reserve pool is the core part of the ESN network, and its parameters are of great significance to the network, including the size of the reserve pool N, the internal connection weight spectrum radius SR of the reserve pool, the input unit scale IS and the sparsity degree SD. Data Science Journal, vol. Recurrent multiplicative neuron model artificial neural network for non-linear time series forecasting. (b) N=Lx×Lx×120 with Lx=10 (circles), 6 (diamonds), and 4 (squares). ESN is improved on the basis of the traditional recurrent neural network. proposed a novel E-KFM model by combining the KFM algorithm and ESN and applied it for multi-step prediction of time sequence data (Xiao et al.

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