Related papers: On the dimension of pullback attractors in recurre…

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 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…

Neural systems are well known for their ability to learn and store information as memories. Even more impressive is their ability to abstract these memories to create complex internal representations, enabling advanced functions such as the…

Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and hence smaller training data sets than competing…

A reservoir computer is a complex dynamical system, often created by coupling nonlinear nodes in a network. The nodes are all driven by a common driving signal. In this work, three dimension estimation methods, false nearest neighbor,…

The aim of this paper is to find an upper bound for the box-counting dimension of uniform attractors for non-autonomous dynamical systems. Contrary to the results in literature, we do not ask the symbol space to have finite box-counting…

Reservoir computing provides a time and cost-efficient alternative to traditional learning methods.Critical regimes, known as the "edge of chaos," have been found to optimize computational performance in binary neural networks. However,…

Reservoir computing approximation and generalization bounds are proved for a new concept class of input/output systems that extends the so-called generalized Barron functionals to a dynamic context. This new class is characterized by the…

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…

Modern predictive modeling increasingly calls for a single learned dynamical substrate to operate across multiple regimes. From a dynamical-systems viewpoint, this capability decomposes into the storage of multiple attractors and the…

Reservoir computing is a popular approach to design recurrent neural networks, due to its training simplicity and approximation performance. The recurrent part of these networks is not trained (e.g., via gradient descent), making them…

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…

Reservoir computing - information processing based on untrained recurrent neural networks with random connections - is expected to depend on the nonlinear properties of the neurons and the resulting oscillatory, chaotic, or fixpoint…

Reservoir computing is a computational framework suited for temporal/sequential data processing. It is derived from several recurrent neural network models, including echo state networks and liquid state machines. A reservoir computing…

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…

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…

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…

We use recent advances in the machine learning area known as 'reservoir computing' to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of…

Reservoir computing typically relies on large, randomly generated reservoirs, enabling simple, often linear readouts. Over the past two decades, most constructions have exploited the freedom to select the reservoir, constrained primarily by…

Physical reservoir computing is a computational framework that offers an energy- and computation-efficient alternative to conventional training of neural networks. In reservoir computing, input signals are mapped into the high-dimensional…