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We introduce a diagonalization-based optimization for Linear Echo State Networks (ESNs) that reduces the per-step computational complexity of reservoir state updates from O(N^2) to O(N). By reformulating reservoir dynamics in the eigenbasis…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-24 Romain de Coudenhove , Yannis Bendi-Ouis , Anthony Strock , Xavier Hinaut

Echo state networks (ESNs) are a class of recurrent neural networks in which only the readout layer is trainable, while the recurrent and input layers are fixed. This architectural constraint enables computationally efficient processing of…

Machine Learning · Computer Science 2025-07-31 Taiki Yamada , Yuichi Katori , Kantaro Fujiwara

Spatio-temporal area-level datasets play a critical role in official statistics, providing valuable insights for policy-making and regional planning. Accurate modeling and forecasting of these datasets can be extremely useful for…

Machine Learning · Computer Science 2026-01-06 Zhenhua Wang , Scott H. Holan , Christopher K. Wikle

In reservoir computing, an input sequence is processed by a recurrent neural network, the reservoir, which transforms it into a spatial pattern that a shallow readout network can then exploit for tasks such as memorization and time-series…

Neural and Evolutionary Computing · Computer Science 2025-12-30 Denis Kleyko , Christopher J. Kymn , E. Paxon Frady , Amy Loutfi , Friedrich T. Sommer

Many natural and physical processes can be understood by analyzing multiple system variables evolving, forming a multivariate time series. Predicting such time series is challenging due to the inherent noise and interdependencies among…

Chaotic Dynamics · Physics 2025-12-11 S. Hariharan , R. Suresh , V. K. Chandrasekar

Stock return prediction is a problem that has received much attention in the finance literature. In recent years, sophisticated machine learning methods have been shown to perform significantly better than ''classical'' prediction…

Computational Finance · Quantitative Finance 2025-04-29 Giovanni Ballarin , Jacopo Capra , Petros Dellaportas

Echo state network (ESN), a kind of recurrent neural networks, consists of a fixed reservoir in which neurons are connected randomly and recursively and obtains the desired output only by training output connection weights. First-order…

Machine Learning · Computer Science 2024-01-22 Yansong Li , Kai Hu , Kohei Nakajima , Yongping Pan

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

Forecasting stock and cryptocurrency prices is challenging due to high volatility and non-stationarity, influenced by factors like economic changes and market sentiment. Previous research shows that Echo State Networks (ESNs) can…

Machine Learning · Computer Science 2025-08-08 Mansi Sharma , Enrico Sartor , Marc Cavazza , Helmut Prendinger

What is a neural model with minimum architectural complexity that exhibits reasonable language learning capability? To explore such a simple but sufficient neural language model, we revisit a basic reservoir computing (RC) model, Echo State…

Computation and Language · Computer Science 2025-03-04 Ryo Ueda , Tatsuki Kuribayashi , Shunsuke Kando , Kentaro Inui

This paper explores the problem of training a recurrent neural network from noisy data. While neural network based dynamic predictors perform well with noise-free training data, prediction with noisy inputs during training phase poses a…

Systems and Control · Electrical Eng. & Systems 2023-04-04 Debdipta Goswami

This paper introduces the NK Echo State Network. The problem of learning in the NK Echo State Network is reduced to the problem of optimizing a special form of a Spin Glass Problem known as an NK Landscape. No weight adjustment is used; all…

Neural and Evolutionary Computing · Computer Science 2015-05-11 Darrell Whitley , Renato Tinós , Francisco Chicano

Study of dynamical systems using partial state observation is an important problem due to its applicability to many real-world systems. We address the problem by studying an echo state network (ESN) framework with partial state input with…

Systems and Control · Electrical Eng. & Systems 2023-12-06 Ajit Mahata , Reetish Padhi , Amit Apte

Modeling the dynamics of the formation and evolution of protostellar disks as well as the history of stellar mass accretion typically involve the numerical solution of complex systems of coupled differential equations. The resulting mass…

Solar and Stellar Astrophysics · Physics 2023-04-18 Gianfranco Bino , Shantanu Basu , Ramit Dey , Sayantan Auddy , Lyle Muller , Eduard I. Vorobyov

Echo State Networks (ESNs) are a reservoir computing framework widely used for nonlinear time-series prediction. However, despite their effectiveness, randomly initialized reservoirs often contain redundant nodes, leading to unnecessary…

Machine Learning · Computer Science 2026-05-07 Sudip Laudari

This paper investigates the performance of Echo State Networks (ESNs) for univariate time series forecasting using a subset of the M4 Forecasting Competition dataset. Focusing on monthly and quarterly time series, we evaluate whether a…

Machine Learning · Computer Science 2026-04-08 Alexander Häußer

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…

Physics and Society · Physics 2019-06-28 Nguyen Anh Khoa Doan , Wolfgang Polifke , Luca Magri

Recurrent neural networks (RNNs) can be interpreted as discrete-time state-space models, where the state evolution corresponds to an infinite-impulse-response (IIR) filtering operation governed by both feedforward weights and recurrent…

Machine Learning · Computer Science 2026-02-26 Alexander Morgan , Ummay Sumaya Khan , Lingjia Liu , Lizhong Zheng

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…

Machine Learning · Computer Science 2020-11-05 Nguyen Anh Khoa Doan , Wolfgang Polifke , Luca Magri

Echo state networks (ESN), a type of reservoir computing (RC) architecture, are efficient and accurate artificial neural systems for time series processing and learning. An ESN consists of a core of recurrent neural networks, called a…

Neural and Evolutionary Computing · Computer Science 2015-04-28 Alireza Goudarzi , Alireza Shabani , Darko Stefanovic