Related papers: Learning Hidden States in a Chaotic System: A Phys…

Echo State Networks (ESNs) are recurrent neural networks usually employed for modeling nonlinear dynamic systems with relatively ease of training. By incorporating physical laws into the training of ESNs, Physics-Informed ESNs (PI-ESNs)…

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…

We propose the Automatic-differentiated Physics-Informed Echo State Network (API-ESN). The network is constrained by the physical equations through the reservoir's exact time-derivative, which is computed by automatic differentiation. As…

We present the Physics-Informed Long Short-Term Memory (PI-LSTM) network to reconstruct and predict the evolution of unmeasured variables in a chaotic system. The training is constrained by a regularization term, which penalizes solutions…

Noise reduction is a relevant topic when considering the application of chaotic signals in practical problems, such as communication systems or modeling biomedical signals. In this paper an echo state network (ESN) is employed to denoise a…

This paper explores the problem of training a recurrent neural network from noisy data. While neural network based dynamic predictors perform well with noise-free training data, prediction with noisy inputs during training phase poses a…

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its…

Among the various architectures of Recurrent Neural Networks, Echo State Networks (ESNs) emerged due to their simplified and inexpensive training procedure. These networks are known to be sensitive to the setting of hyper-parameters, which…

Machine learning methods have shown promise in learning chaotic dynamical systems, enabling model-free short-term prediction and attractor reconstruction. However, when applied to large-scale, spatiotemporally chaotic systems, purely…

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…

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 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…

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…

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…

Echo state network (ESN), a kind of recurrent neural networks, consists of a fixed reservoir in which neurons are connected randomly and recursively and obtains the desired output only by training output connection weights. First-order…

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when…

This paper proposes a novel and interpretable recurrent neural-network structure using the echo-state network (ESN) paradigm for time-series prediction. While the traditional ESNs perform well for dynamical systems prediction, it needs a…

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…