Related papers: Separation of Chaotic Signals by Reservoir Computi…

Controlling nonlinear dynamical systems using machine learning allows to not only drive systems into simple behavior like periodicity but also to more complex arbitrary dynamics. For this, it is crucial that a machine learning system can be…

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 natural hypothesis for the success of reservoir computing in generic tasks is the ability of the untrained reservoir to map different input time series to separable reservoir states - a property we term separation capacity. We provide a…

This paper studies numerically how the signal detector arrangement influences the performance of reservoir computing using spin waves excited in a ferrimagnetic garnet film. This investigation is essentially important since the input…

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…

We develop a versatile optimization method, which finds the design parameters that minimize time-averaged acoustic cost functionals. The method is gradient-free, model-informed, and data-driven with reservoir computing based on echo state…

The output of oscillators is usually not stable over time. In particular, phase variations---or \emph{phase noise}---corrupts the oscillations. In this letter, we describe a circuit that designed to average the phase noise processes and…

We investigate seismic motion propagation through a passively isolated mechanical system, using Wiener filters and convolutional neural networks with time-dilation layers. The goal of this study was to explore the capabilities of neural…

Noise reduction is a relevant topic when considering the application of chaotic signals in practical problems, such as communication systems or modeling biomedical signals. In this paper an echo state network (ESN) is employed to denoise a…

We demonstrate that transformers obtain impressive performance even when some of the layers are randomly initialized and never updated. Inspired by old and well-established ideas in machine learning, we explore a variety of non-linear…

We present an efficient particle filtering algorithm for multiscale systems, that is adapted for simple atmospheric dynamics models which are inherently chaotic. Particle filters represent the posterior conditional distribution of the state…

There is a wave of interest in using unsupervised neural networks for solving differential equations. The existing methods are based on feed-forward networks, {while} recurrent neural network differential equation solvers have not yet been…

Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode…

Forecasting chaotic time series requires models that can capture the intrinsic geometry of the underlying attractor while remaining computationally efficient. We introduce a novel reservoir computing (RC) framework that integrates…

Quantitative evaluations of differences and/or similarities between data samples define and shape optimisation problems associated with learning data distributions. Current methods to compare data often suffer from limitations in capturing…

In this paper, we present an optimal filter for linear time-varying continuous-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense. We first show that the unknown inputs…

The decomposition of a stochastic time series into three component series representing a dual signal - namely, the mean and dispersion - while isolating noise is presented. The decomposition is performed by applying machine learning…

Forecasting the dynamics of large complex networks from previous time-series data is important in a wide range of contexts. Here we present a machine learning scheme for this task using a parallel architecture that mimics the topology of…

For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…

In the 1940s, Wiener introduced a linear predictor, where the future prediction is computed by linearly combining the past data. A transformer generalizes this idea: it is a nonlinear predictor where the next-token prediction is computed by…