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Echo State Network (ESN) presents a distinguished kind of recurrent neural networks. It is built upon a sparse, random and large hidden infrastructure called reservoir. ESNs have succeeded in dealing with several non-linear problems such as…

Neural and Evolutionary Computing · Computer Science 2018-06-12 Naima Chouikhi , Boudour Ammar , Adel M. Alimi

An Echo State Network (ESN) is a type of single-layer recurrent neural network with randomly-chosen internal weights and a trainable output layer. We prove under mild conditions that a sufficiently large Echo State Network can approximate…

Dynamical Systems · Mathematics 2021-06-28 Allen G. Hart , Kevin R. Olding , A. M. G. Cox , Olga Isupova , J. H. P. Dawes

Echo State Networks (ESNs) are widely-used Recurrent Neural Networks. They are dynamical systems including, in state-space form, a nonlinear state equation and a linear output transformation. The common procedure to train ESNs is to…

Systems and Control · Electrical Eng. & Systems 2019-12-05 Luca Bugliari Armenio , Lorenzo Fagiano , Enrico Terzi , Marcello Farina , Riccardo Scattolini

Echo State Networks (ESNs) are a special type of recurrent neural networks (RNNs), in which the input and recurrent connections are traditionally generated randomly, and only the output weights are trained. Despite the recent success of…

Machine Learning · Computer Science 2022-05-11 Peter Steiner , Azarakhsh Jalalvand , Peter Birkholz

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its…

Statistical Mechanics · Physics 2024-12-17 Clement Dinh , Yunhao Fan , Gia-Wei Chern

As one of the most important paradigms of recurrent neural networks, the echo state network (ESN) has been applied to a wide range of fields, from robotics to medicine, finance, and language processing. A key feature of the ESN paradigm is…

Machine Learning · Computer Science 2020-02-26 Pau Vilimelis Aceituno , Yan Gang , Yang-Yu Liu

Parameter updating is an important stage in parallelism-based distributed deep learning. Synchronous methods are widely used in distributed training the Deep Neural Networks (DNNs). To reduce the communication and synchronization overhead…

Machine Learning · Computer Science 2020-09-09 Qing Ye , Yuxuan Han , Yanan sun , JIancheng Lv

Echo state networks (ESNs) are a powerful form of reservoir computing that only require training of linear output weights whilst the internal reservoir is formed of fixed randomly connected neurons. With a correctly scaled connectivity…

Machine Learning · Computer Science 2021-08-03 Luca Manneschi , Matthew O. A. Ellis , Guido Gigante , Andrew C. Lin , Paolo Del Giudice , Eleni Vasilaki

A particular case of Recurrent Neural Network (RNN) was introduced at the beginning of the 2000s under the name of Echo State Networks (ESNs). The ESN model overcomes the limitations during the training of the RNNs while introducing no…

Machine Learning · Computer Science 2015-01-06 Sebastián Basterrech

Among the various architectures of Recurrent Neural Networks, Echo State Networks (ESNs) emerged due to their simplified and inexpensive training procedure. These networks are known to be sensitive to the setting of hyper-parameters, which…

Neural and Evolutionary Computing · Computer Science 2019-09-23 Pietro Verzelli , Cesare Alippi , Lorenzo Livi

Deep learning has been successfully applied in several fields such as machine translation, manufacturing, and pattern recognition. However, successful application of deep learning depends upon appropriately setting its parameters to achieve…

Neural and Evolutionary Computing · Computer Science 2017-11-29 Basheer Qolomany , Majdi Maabreh , Ala Al-Fuqaha , Ajay Gupta , Driss Benhaddou

The Echo State Network (ESN) is a class of Recurrent Neural Network with a large number of hidden-hidden weights (in the so-called reservoir). Canonical ESN and its variations have recently received significant attention due to their…

Neural and Evolutionary Computing · Computer Science 2022-09-30 Sebastian Basterrech , Gerardo Rubino

Recurrent Neural Networks (RNNs) have demonstrated their outstanding ability in sequence tasks and have achieved state-of-the-art in wide range of applications, such as industrial, medical, economic and linguistic. Echo State Network (ESN)…

Machine Learning · Computer Science 2020-12-08 Chenxi Sun , Moxian Song , Shenda Hong , Hongyan Li

Echo State Networks (ESNs) are typically presented as efficient, readout-trained recurrent models, yet their dynamics and design are often guided by heuristics rather than first principles. We recast ESNs explicitly as state-space models…

Machine Learning · Computer Science 2025-09-05 Pradeep Singh , Balasubramanian Raman

The goal of this paper is to investigate the theoretical properties, the training algorithm, and the predictive control applications of Echo State Networks (ESNs), a particular kind of Recurrent Neural Networks. First, a condition…

Systems and Control · Computer Science 2019-02-06 Luca Bugliari Armenio , Enrico Terzi , Marcello Farina , Riccardo Scattolini

Physics-informed neural networks (PINN) have recently emerged as a promising application of deep learning in a wide range of engineering and scientific problems based on partial differential equation (PDE) models. However, evidence shows…

Machine Learning · Computer Science 2022-10-24 Caio Davi , Ulisses Braga-Neto

It is a widely accepted fact that data representations intervene noticeably in machine learning tools. The more they are well defined the better the performance results are. Feature extraction-based methods such as autoencoders are…

Neural and Evolutionary Computing · Computer Science 2018-06-12 Naima Chouikhi , Boudour Ammar , Adel M. Alimi

Nature has long inspired the development of swarm intelligence (SI), a key branch of artificial intelligence that models collective behaviors observed in biological systems for solving complex optimization problems. Particle swarm…

Neural and Evolutionary Computing · Computer Science 2025-11-18 Dikshit Chauhan , Shivani , P. N. Suganthan

Convolutional neural networks (CNNs) are one of the most effective deep learning methods to solve image classification problems, but the best architecture of a CNN to solve a specific problem can be extremely complicated and hard to design.…

Neural and Evolutionary Computing · Computer Science 2018-03-20 Bin Wang , Yanan Sun , Bing Xue , Mengjie Zhang

Echo State Networks (ESNs) are recurrent neural networks usually employed for modeling nonlinear dynamic systems with relatively ease of training. By incorporating physical laws into the training of ESNs, Physics-Informed ESNs (PI-ESNs)…

Machine Learning · Computer Science 2025-02-05 Eric Mochiutti , Eric Aislan Antonelo , Eduardo Camponogara
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