Related papers: A local Echo State Property through the largest Ly…

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 (ML) is widely used to model chaotic systems. Among ML approaches, echo state networks (ESNs) have received considerable attention due to their simple construction and fast training. However, ESN performance is highly…

Recognising previously visited locations is an important, but unsolved, task in autonomous navigation. Current visual place recognition (VPR) benchmarks typically challenge models to recover the position of a query image (or images) from…

We use recent advances in the machine learning area known as 'reservoir computing' to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of…

Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is…

In the last decade, a new computational paradigm was introduced in the field of Machine Learning, under the name of Reservoir Computing (RC). RC models are neural networks which a recurrent part (the reservoir) that does not participate in…

Using data from mobile network utilization in Norway, we showcase the possibility of monitoring the state of communication and mobility networks with a non-invasive, low-cost method. This method transforms the network data into a model…

Long-lead forecasting for spatio-temporal systems can often entail complex nonlinear dynamics that are difficult to specify it a priori. Current statistical methodologies for modeling these processes are often highly parameterized and thus,…

We present a rigorous asymptotic analysis of Echo State Networks (ESNs) in a teacher student setting with a linear teacher with oracle weights. Leveraging random matrix theory, we derive closed form expressions for the asymptotic bias,…

In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before…

In the field of complex dynamics, multistable attractors have been gaining a significant attention due to its unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse…

Reservoir computing is a machine learning framework that has been shown to be able to replicate the chaotic attractor, including the fractal dimension and the entire Lyapunov spectrum, of the dynamical system on which it is trained. We…

Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…

We propose a deep architecture for the classification of multivariate time series. By means of a recurrent and untrained reservoir we generate a vectorial representation that embeds temporal relationships in the data. To improve the…

Recurrent neural networks are machine learning algorithms which are suited well to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by…

This paper presents a method for reproducing a simple central pattern generator (CPG) using a modified Echo State Network (ESN). Conventionally, the dynamical reservoir needs to be damped to stabilize and preserve memory. However, we find…

Background/introduction: Cross-Validation (CV) is still uncommon in time series modeling. Echo State Networks (ESNs), as a prime example of Reservoir Computing (RC) models, are known for their fast and precise one-shot learning, that often…

In recent years, more and more works have appeared devoted to the analog (hardware) implementation of artificial neural networks, in which neurons and the connection between them are based not on computer calculations, but on physical…

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…

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…