Related papers: Deep Learning of Conjugate Mappings
A general procedure which defines a partial ordering of cyclic permutations induced by continuous maps is known for constructing immediate successors to a cycle. We expound on this procedure in terms of labelled digraphs and characteristic…
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…
We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…
Advances in machine learning have revolutionized capabilities in applications ranging from natural language processing to marketing to health care. Here, we demonstrate the efficacy of machine learning in predicting chaotic behavior in…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
Controlling nonlinear dynamics is a long-standing problem in engineering. Harnessing known physical information to accelerate or constrain stochastic learning pursues a new paradigm of scientific machine learning. By linearizing nonlinear…
Generic Hamiltonian systems have a mixed phase space, where classically disjoint regions of regular and chaotic motion coexist. We present an iterative method to construct an integrable approximation, which resembles the regular dynamics of…
Discovering governing equations from data, in particular high dimensional data, is challenging in various fields of science and engineering, and it has potential to revolutionise the science and technology in this big data era. This paper…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
In this work, we are interested in structure learning for a set of spatially distributed dynamical systems, where individual subsystems are coupled via latent variables and observed through a filter. We represent this model as a directed…
In chaotic dynamical systems, a number of rare trajectories with low level of chaoticity are embedded in chaotic sea, while extraordinary unstable trajectories can exist even in weakly chaotic regions. In this study, a quantitative method…
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.,…
Recently Chen and Poor initiated the study of learning mixtures of linear dynamical systems. While linear dynamical systems already have wide-ranging applications in modeling time-series data, using mixture models can lead to a better fit…
Intriguing routes to chaos have been experimentally observed in semiconductor superlattices driven by an ac field. In this work, a theoretical model of time dependent transport in ac driven superlattices is numerically solved. In agreement…
Chaotic dynamical systems (DS) are ubiquitous in nature and society. Often we are interested in reconstructing such systems from observed time series for prediction or mechanistic insight, where by reconstruction we mean learning…
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…
Many interesting physical systems have mathematical descriptions as finite-dimensional or infinite-dimensional Hamiltonian systems. Poincare who started the modern theory of dynamical systems and symplectic geometry developed a particular…