Related papers: Improved Long-Term Prediction of Chaos Using Reser…

Recently, machine learning techniques, particularly deep learning, have demonstrated superior performance over traditional time series forecasting methods across various applications, including both single-variable and multi-variable…

A reservoir computer (RC) is a type of simplified recurrent neural network architecture that has demonstrated success in the prediction of spatiotemporally chaotic dynamical systems. A further advantage of RC is that it reproduces intrinsic…

Deducing the states of spatiotemporally chaotic systems (SCSs) as they evolve in time is crucial for various applications. However, it is a dramatic challenge for generally achieving so due to the complexity of non-periodic dynamics and the…

Reduced-order dynamical models play a central role in developing our understanding of predictability of climate irrespective of whether we are dealing with the actual climate system or surrogate climate-models. In this context, the…

Reservoir computing (RC) is a powerful framework for predicting nonlinear dynamical systems, yet the role of reservoir topology$-$particularly symmetry in connectivity and weights$-$remains not adequately understood. This work investigates…

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…

The prediction of time series is a challenging task relevant in such diverse applications as analyzing financial data, forecasting flow dynamics or understanding biological processes. Especially chaotic time series that depend on a long…

Using the machine learning approach known as reservoir computing, it is possible to train one dynamical system to emulate another. We show that such trained reservoir computers reproduce the properties of the attractor of the chaotic system…

Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has…

Forecasting chaotic systems is a notably complex task, which in recent years has been approached with reasonable success using reservoir computing (RC), a recurrent network with fixed random weights (the reservoir) used to extract the…

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 has proven effective for tasks such as time-series prediction, particularly in the context of chaotic systems. However, conventional reservoir computing frameworks often face challenges in achieving high prediction…

To predict the future evolution of dynamical systems purely from observations of the past data is of great potential application. In this work, a new formulated paradigm of reservoir computing is proposed for achieving model-free…

Physical reservoir computing (RC) is a machine learning algorithm that employs the dynamics of a physical system to forecast highly nonlinear and chaotic phenomena. In this paper, we introduce a quantum RC system that employs the dynamics…

Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle large systems. Its implementation, however, often requires full state-vector measurements and…

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of…

Prediction of spatio-temporal chaotic systems is important in various fields, such as Numerical Weather Prediction (NWP). While data assimilation methods have been applied in NWP, machine learning techniques, such as Reservoir Computing…

The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir Computing and Normalizing Flow to study this issue, which…

Machine learning has become a fundamental approach for modeling, prediction, and control, enabling systems to learn from data and perform complex tasks. Reservoir computing is a machine learning tool that leverages high-dimensional…

In this study, we have shown autonomous long-term prediction with a spintronic physical reservoir. Due to the short-term memory property of the magnetization dynamics, non-linearity arises in the reservoir states which could be used for…