Related papers: Automatic-differentiated Physics-Informed Echo Sta…

We propose a physics-informed machine learning method to predict the time average of a chaotic attractor. The method is based on the hybrid echo state network (hESN). We assume that the system is ergodic, so the time average is equal to the…

An approach to the time-accurate prediction of chaotic solutions is by learning temporal patterns from data. Echo State Networks (ESNs), which are a class of Reservoir Computing, can accurately predict the chaotic dynamics well beyond the…

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…

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…

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 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…

A reservoir computer is a special type of neural network, where most of the weights are randomly fixed and only a subset are trained. In this thesis we prove results about reservoir computers trained on deterministic dynamical systems, and…

In real-world applications such as emotion recognition from recorded brain activity, data are captured from electrodes over time. These signals constitute a multidimensional time series. In this paper, Echo State Network (ESN), a recurrent…

Aero-engine fault prediction aims to accurately predict the development trend of the future state of aero-engines, so as to diagnose faults in advance. Traditional aero-engine parameter prediction methods mainly use the nonlinear mapping…

Reservoir Computing has found many potential applications in the field of complex dynamics. In this article, we exploit the exceptional capability of the echo-state network (ESN) model to make it learn a unidirectional coupling scheme from…

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…

At the heart of time-series forecasting (TSF) lies a fundamental challenge: how can models efficiently and effectively capture long-range temporal dependencies across ever-growing sequences? While deep learning has brought notable progress,…

This paper considers the problem of data-driven prediction of partially observed systems using a recurrent neural network. While neural network based dynamic predictors perform well with full-state training data, prediction with partial…

We propose an innovative design for an optical Echo State Network (ESN), an advanced type of reservoir computer known for its universal computational capabilities. Our design enables an optical implementation of arbitrary ESNs, featuring…

This work builds an automated anomaly detection method for chaotic time series, and more concretely for turbulent, high-dimensional, ocean simulations. We solve this task by extending the Echo State Network by spatially aware input maps,…

Echo State Networks (ESNs) are recurrent neural networks that only train their output layer, thereby precluding the need to backpropagate gradients through time, which leads to significant computational gains. Nevertheless, a common issue…

Spatio-temporal data and processes are prevalent across a wide variety of scientific disciplines. These processes are often characterized by nonlinear time dynamics that include interactions across multiple scales of spatial and temporal…

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…

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…

In the framework of physical reservoir computing (RC), machine learning algorithms designed for digital computers are executed using analog computer-like nonlinear physical systems that can provide energy-efficient computational power for…