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Global climate models are essential tools to simulate past and potential future pathways of climate change, as well as associated climate impacts. Shared Socioeconomic Pathways (SSPs) describe a range of future scenarios of global economic…

Machine Learning · Computer Science 2026-05-19 Graham Clyne , Julia Kaltenborn , Peer Nowack , Claire Monteleoni , Anasatase Charantonis

We propose Echo State Networks (ESNs) to predict the statistics of extreme events in a turbulent flow. We train the ESNs on small datasets that lack information about the extreme events. We asses whether the networks are able to extrapolate…

Fluid Dynamics · Physics 2022-04-13 Alberto Racca , Luca Magri

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

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

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

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

Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand…

Machine Learning · Computer Science 2020-02-18 Peter Tino

Echo State Networks (ESNs) are simplified recurrent neural network models composed of a reservoir and a linear, trainable readout layer. The reservoir is tunable by some hyper-parameters that control the network behaviour. ESNs are known to…

Neural and Evolutionary Computing · Computer Science 2018-11-06 Pietro Verzelli , Lorenzo Livi , Cesare Alippi

We introduce an interpretable-by-design method, optimized model-analog, that integrates deep learning with model-analog forecasting which generates forecasts from similar initial climate states in a repository of model simulations. This…

Atmospheric and Oceanic Physics · Physics 2024-10-10 Kinya Toride , Matthew Newman , Andrew Hoell , Antonietta Capotondi , Jakob Schlör , Dillon J. Amaya

The unprecedented dissemination of edge devices is accompanied by a growing demand for neuromorphic chips that can process time-series data natively without cloud support. Echo state network (ESN) is a class of recurrent neural networks…

Machine Learning · Computer Science 2025-03-04 Abdullah M. Zyarah , Alaa M. Abdul-Hadi , Dhireesha Kudithipudi

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

The El Ni\~no Southern Oscillation (ENSO) is the dominant driver of interannual global climate variability and can lead to extreme weather events such as droughts or flooding. Recently, we have developed several statistical approaches for…

Atmospheric and Oceanic Physics · Physics 2026-02-17 Josef Ludescher , Jun Meng , Jingfang Fan , Armin Bunde , Hans Joachim Schellnhuber

Echo State Networks (ESNs) are time-series processing models working under the Echo State Property (ESP) principle. The ESP is a notion of stability that imposes an asymptotic fading of the memory of the input. On the other hand, the…

Machine Learning · Computer Science 2023-09-06 Andrea Ceni , Claudio Gallicchio

This article introduces a robust hybrid method for solving supervised learning tasks, which uses the Echo State Network (ESN) model and the Particle Swarm Optimization (PSO) algorithm. An ESN is a Recurrent Neural Network with the…

Neural and Evolutionary Computing · Computer Science 2015-01-05 Sebastián Basterrech , Enrique Alba , Václav Snášel

We present a study using a class of post-hoc local explanation methods i.e., feature importance methods for "understanding" a deep learning (DL) emulator of climate. Specifically, we consider a multiple-input-single-output emulator that…

Machine Learning · Computer Science 2021-08-31 Wei Xu , Xihaier Luo , Yihui Ren , Ji Hwan Park , Shinjae Yoo , Balasubramanya T. Nadiga

The development of robust Early Warning Signals (EWS) is necessary to quantify the risk of crossing tipping points in the present-day climate change. Classically, EWS are statistical measures based on time series of climate state variables,…

Atmospheric and Oceanic Physics · Physics 2025-03-25 Laure Moinat , Jérôme Kasparian , Maura Brunetti

The impacts of climate change are felt by most critical systems, such as infrastructure, ecological systems, and power-plants. However, contemporary Earth System Models (ESM) are run at spatial resolutions too coarse for assessing effects…

Computer Vision and Pattern Recognition · Computer Science 2017-03-10 Thomas Vandal , Evan Kodra , Sangram Ganguly , Andrew Michaelis , Ramakrishna Nemani , Auroop R Ganguly

Then detection and identification of extreme weather events in large-scale climate simulations is an important problem for risk management, informing governmental policy decisions and advancing our basic understanding of the climate system.…

Computer Vision and Pattern Recognition · Computer Science 2017-11-28 Evan Racah , Christopher Beckham , Tegan Maharaj , Samira Ebrahimi Kahou , Prabhat , Christopher Pal

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

Extreme event are sudden large-amplitude changes in the state or observables of chaotic nonlinear systems, which characterize many scientific phenomena. Because of their violent nature, extreme events typically have adverse consequences,…

Machine Learning · Computer Science 2023-08-08 Alberto Racca , Luca Magri