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Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems…

This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible…

Whereas the power of reservoir computing (RC) in inferring chaotic systems has been well established in the literature, the studies are mostly restricted to mono-functional machines where the training and testing data are acquired from the…

We propose and demonstrate a nonlinear control method that can be applied to unknown, complex systems where the controller is based on a type of artificial neural network known as a reservoir computer. In contrast to many modern…

We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…

Reservoir Computing is an emerging machine learning framework which is a versatile option for utilising physical systems for computation. In this paper, we demonstrate how a single node reservoir, made of a simple electronic circuit, can be…

We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its…

The prediction of complex nonlinear dynamical systems with the help of machine learning techniques has become increasingly popular. In particular, reservoir computing turned out to be a very promising approach especially for the…

Reservoir computing is a machine learning paradigm that uses a structure called a reservoir, which has nonlinearities and short-term memory. In recent years, reservoir computing has expanded to new functions such as the autonomous…

We show that a reservoir computer is an effective tool for model-free prediction of extreme events in deterministic chaotic systems. This prediction allows us to suppress unwanted extreme events, by applying weak control perturbations to…

Reservoir computing has emerged as a powerful framework for time series modelling and forecasting including the prediction of discontinuous transitions. However, the mechanism behind its success is not yet fully understood. This letter…

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…

Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture…

Can a neural network trained by the time series of system A be used to predict the evolution of system B? This problem, knowing as transfer learning in a broad sense, is of great importance in machine learning and data mining, yet has not…

Recent research has demonstrated Reservoir Computing's capability to model various chaotic dynamical systems, yet its application to Hamiltonian systems remains relatively unexplored. This paper investigates the effectiveness of Reservoir…

Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from…

Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to…

Several recent papers have shown that reservoir computers are useful for analyzing and predicting dynamical systems. Reservoir computers have also been shown to be useful for various classification problems. In this work, a reservoir…

We demonstrate a data-driven technique for adaptive control in dynamical systems that exploits the reservoir computing method. We show that a reservoir computer can be trained to predict a system parameter from the time series data.…

In applications, an anticipated situation is where the system of interest has never been encountered before and sparse observations can be made only once. Can the dynamics be faithfully reconstructed from the limited observations without…