Recently, a layer-stacked ESN model named deep echo state network (DeepESN) has been established. As an interactional model of a recurrent neural network and deep neural network, investigations of DeepESN are of significant importance in both areas. Optimizing the structure of neural networks remains a common task in artificial neural networks, and the question of how many neurons should be used in each layer of DeepESN must be stressed. In this paper, our aim is to solve the problem of

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... the optimized size of DeepESN. Inspired by the sensitive iterative pruning algorithm, a neuronal similarity-based iterative pruning merging algorithm (NS-IPMA) is proposed to iteratively prune or merge the most similar neurons in DeepESN. Two chaotic time series prediction tasks are applied to demonstrate the effectiveness of NS-IPMA. The results show that the DeepESN pruned by NS-IPMA outperforms the unpruned DeepESN with the same network size, and NS-IPMA is a feasible and superior approach to improving the generalization performance of DeepESN. The newly proposed method has broad application prospects in real-time systems.