Related papers: Robust Optimization and Validation of Echo State N…

In many real-world applications, fully-differentiable RNNs such as LSTMs and GRUs have been widely deployed to solve time series learning tasks. These networks train via Backpropagation Through Time, which can work well in practice but…

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…

The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…

As an efficient recurrent neural network (RNN) model, reservoir computing (RC) models, such as Echo State Networks, have attracted widespread attention in the last decade. However, while they have had great success with time series data…

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 study of deep recurrent neural networks (RNNs) and, in particular, of deep Reservoir Computing (RC) is gaining an increasing research attention in the neural networks community. The recently introduced Deep Echo State Network (DeepESN)…

Causal discovery between collections of time-series data can help diagnose causes of symptoms and hopefully prevent faults before they occur. However, reliable causal discovery can be very challenging, especially when the data acquisition…

Reservoir Computing (RC) is a popular methodology for the efficient design of Recurrent Neural Networks (RNNs). Recently, the advantages of the RC approach have been extended to the context of multi-layered RNNs, with the introduction of…

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,…

We propose an approximation of Echo State Networks (ESN) that can be efficiently implemented on digital hardware based on the mathematics of hyperdimensional computing. The reservoir of the proposed integer Echo State Network (intESN) is a…

Continuous Time Echo State Networks (CTESNs) are a promising yet under-explored surrogate modeling technique for dynamical systems, particularly those governed by stiff Ordinary Differential Equations (ODEs). A key determinant of the…

In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we…

Despite their success, deep networks have been shown to be highly susceptible to perturbations, often causing significant drops in accuracy. In this paper, we investigate model robustness on perturbed inputs by studying the performance of…

The data-driven learning of solutions of partial differential equations can be based on a divide-and-conquer strategy. First, the high dimensional data is compressed to a latent space with an autoencoder; and, second, the temporal dynamics…

While Large Language Models and their underlying Transformer architecture are remarkably efficient, they do not reflect how our brain processes and learns a diversity of cognitive tasks such as language, nor how it leverages working memory.…

In this study, we use a reservoir computing based echo state network (ESN) to predict the collective burst synchronization of neurons. Specifically, we investigate the ability of ESN in predicting the burst synchronization of an ensemble of…

Inspired by recent theoretical arguments, physics-informed echo state network (ESN) is discussed on the attempt to train a reservoir model absolutely in physics-informed manner. As the plainest work on such a purpose, an ODE (ordinary…

The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of…

Emergent behaviors are in the focus of recent research interest. It is then of considerable importance to investigate what optimizations suit the learning and prediction of chaotic systems, the putative candidates for emergence. We have…

Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal…