Related papers: Physics-Informed Echo State Networks for Chaotic S…
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…
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,…
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…
Extreme event are sudden large-amplitude changes in the state or observables of chaotic nonlinear systems, which characterize many scientific phenomena. Because of their violent nature, extreme events typically have adverse consequences,…
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…
Echo state networks are powerful recurrent neural networks. However, they are often unstable and shaky, making the process of finding an good ESN for a specific dataset quite hard. Obtaining a superb accuracy by using the Echo State Network…
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…
This paper proposes a control strategy consisting of a robust controller and an Echo State Network (ESN) based control law for stabilizing a class of uncertain nonlinear discrete-time systems subject to persistent disturbances. Firstly, the…
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…
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…
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…
This paper introduces a physics-informed machine learning approach for pathloss prediction. This is achieved by including in the training phase simultaneously (i) physical dependencies between spatial loss field and (ii) measured pathloss…
Prediction based on Irregularly Sampled Time Series (ISTS) is of wide concern in the real-world applications. For more accurate prediction, the methods had better grasp more data characteristics. Different from ordinary time series, ISTS is…
Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both…
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 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…
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…
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…
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…
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…