Related papers: Data-driven prediction and analysis of chaotic ori…

Recently, there has been significant advancement in the machine learning (ML) approach and its application to diverse systems ranging from complex to quantum systems. As one of such systems, a coupled-oscillators system exhibits intriguing…

We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish,…

Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e.,…

This work focuses on developing a data-driven framework using Koopman operator theory for system identification and linearization of nonlinear systems for control. Our proposed method presents a deep learning framework with recursive…

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 study of plasma physics under conditions of extreme temperatures, densities and electromagnetic field strengths is significant for our understanding of astrophysics, nuclear fusion and fundamental physics. These extreme physical systems…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

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…

When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…

Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…

Chaotic systems, such as turbulent flows, are ubiquitous in science and engineering. However, their study remains a challenge due to the large range scales, and the strong interaction with other, often not fully understood, physics. As a…

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…

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…

Neural networks can be used to identify phases and phase transitions in condensed matter systems via supervised machine learning. Readily programmable through modern software libraries, we show that a standard feed-forward neural network…

Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural…

We present that, instead of establishing the equations of motion, one can model-freely reveal the dynamical properties of a black-box system using a learning machine. Trained only by a segment of time series of a state variable recorded at…

We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple…

Deep learning (DL) has achieved great success in many applications, but it has been less well analyzed from the theoretical perspective. The unexplainable success of black-box DL models has raised questions among scientists and promoted the…