相关论文: Variability of echo state network prediction horiz…

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…

Systems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is…

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…

The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability…

We investigate the ability of an ensemble reservoir computing approach to predict the long-term behaviour of the phase-space region in which the motion of charged particles in hadron storage rings is bounded, the so-called dynamic aperture.…

The El Ni\~{n}o-Southern Oscillation (ENSO) is a dominant mode of interannual climate variability, yet the mechanisms limiting its long-lead predictability remain unclear. Here we develop a physics-guided Deep Echo State Network (DESN) that…

Reservoir computing, using nonlinear dynamical systems, offers a cost-effective alternative to neural networks for complex tasks involving processing of sequential data, time series modeling, and system identification. Echo state networks…

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…

We present a data-driven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the…

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…

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…

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…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

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…

In this paper, we explore the predictive capabilities of echo state networks (ESNs) for the generalized Kuramoto-Sivashinsky (gKS) equation, an archetypal nonlinear PDE that exhibits spatiotemporal chaos. Our research focuses on predicting…

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…

We explore the influence of precision of the data and the algorithm for the simulation of chaotic dynamics by neural networks techniques. For this purpose, we simulate the Lorenz system with different precisions using three different neural…

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…

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…

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…