Related papers: Using Machine Learning to Replicate Chaotic Attrac…

Reservoir computing is a powerful framework for modeling dynamical systems due to its universality and computational efficiency. However, a major challenge is achieving a forecast with accurate long-time statistics, or climate, which is…

In chaotic dynamical systems such as the weather, prediction errors grow faster in some situations than in others. Real-time knowledge about the error growth could enable strategies to adjust the modelling and forecasting infrastructure…

Reservoir computing is a machine learning framework that has been shown to be able to replicate the chaotic attractor, including the fractal dimension and the entire Lyapunov spectrum, of the dynamical system on which it is trained. We…

A machine-learning approach called "reservoir computing" has been used successfully for short-term prediction and attractor reconstruction of chaotic dynamical systems from time series data. We present a theoretical framework that describes…

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 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…

Recent theoretical developments of reservoir computing have clarified a sufficient condition about which reservoir computing can capture the dynamics of a target system, enabling the reconstruction of dynamical invariants. Even when 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…

Understanding and quantifying chaos from data remains challenging. We present a data-driven method for estimating the largest Lyapunov exponent (LLE) from one-dimensional chaotic time series using machine learning. A predictor is trained to…

This study covers an analytical approach to calculate positively invariant sets of dynamical systems. Using Lyapunov techniques and quantifier elimination methods, an automatic procedure for determining bounds in the state space as an…

Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy, as well as reconstruct the general properties of a…

Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal…

The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…

In this article we study if a Deep Learning technique can be used to obtain an approximated value of the Lyapunov exponents of a dynamical system. Moreover, we want to know if Machine Learning techniques are able, once trained, to provide…

Reservoir computing is a recently introduced machine learning paradigm that has been shown to be well-suited for the processing of spatiotemporal data. Rather than training the network node connections and weights via backpropagation in…

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…

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…

We propose a physics-constrained machine learning method-based on reservoir computing- to time-accurately predict extreme events and long-term velocity statistics in a model of turbulent shear flow. The method leverages the strengths of two…

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…