Related papers: Model-free inference of unseen attractors: Reconst…

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…

Photonic reservoir computing has been successfully utilized in time-series prediction as the need for hardware implementations has increased. Prediction of chaotic time series remains a significant challenge, an area where the conventional…

A new machine learning scheme, termed versatile reservoir computing, is proposed for sustaining the dynamics of heterogeneous complex networks. We show that a single, small-scale reservoir computer trained on time series from a subset 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…

Multifunctionality is a well observed phenomenological feature of biological neural networks and considered to be of fundamental importance to the survival of certain species over time. These multifunctional neural networks are capable of…

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…

Measurements acquired from distributed physical systems are often sparse and noisy. Therefore, signal processing and system identification tools are required to mitigate noise effects and reconstruct unobserved dynamics from limited sensor…

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…

Chaotic dynamics are ubiquitous in nature and useful in engineering, but their geometric design can be challenging. Here, we propose a method using reservoir computing to generate chaos with a desired shape by providing a periodic orbit as…

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…

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…

A new explanation of geometric nature of the reservoir computing phenomenon is presented. Reservoir computing is understood in the literature as the possibility of approximating input/output systems with randomly chosen recurrent neural…

This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…

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…

Efficient and accurate prediction of physical systems is important even when the rules of those systems cannot be easily learned. Reservoir computing, a type of recurrent neural network with fixed nonlinear units, is one such prediction…

We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the system flow. The input to the method is…

We demonstrate the utility of machine learning in the separation of superimposed chaotic signals using a technique called Reservoir Computing. We assume no knowledge of the dynamical equations that produce the signals, and require only…

A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.

Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up…

Typical amortized inference in variational autoencoders is specialized for a single probabilistic query. Here we propose an inference network architecture that generalizes to unseen probabilistic queries. Instead of an encoder-decoder pair,…