Related papers: Deep Learning of Chaos Classification
Lagrangian descriptors (LDs) based on the arc length of orbits previously demonstrated their utility in delineating structures governing the dynamics. Recently, a chaos indicator based on the second derivatives of the LDs, referred to as…
Traditional algorithms to optimize artificial neural networks when confronted with a supervised learning task are usually exploitation-type relaxational dynamics such as gradient descent (GD). Here, we explore the dynamics of the neural…
We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to…
Deep networks are commonly used to model dynamical systems, predicting how the state of a system will evolve over time (either autonomously or in response to control inputs). Despite the predictive power of these systems, it has been…
Modern neural network architectures for large-scale learning tasks have substantially higher model complexities, which makes understanding, visualizing and training these architectures difficult. Recent contributions to deep learning…
We investigate the use of Deep Neural Networks for the classification of image datasets where texture features are important for generating class-conditional discriminative representations. To this end, we first derive the size of the…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
Deep reinforcement learning agents achieve state-of-the-art performance in a wide range of simulated control tasks. However, successful applications to real-world problems remain limited. One reason for this dichotomy is because the learnt…
In this paper, we discuss the Lyapunov exponent definition of chaos and how it can be used to quantify the chaotic behavior of a system. We derive a way to practically calculate the Lyapunov exponent of a one-dimensional system and use it…
The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…
Generating long-term trajectories of dissipative chaotic systems autoregressively is a highly challenging task. The inherent positive Lyapunov exponents amplify prediction errors over time. Many chaotic systems possess a crucial property -…
We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered…
We consider dynamical and geometrical aspects of deep learning. For many standard choices of layer maps we display semi-invariant metrics which quantify differences between data or decision functions. This allows us, when considering random…
Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…
Dynamics in biological networks are in general robust against several perturbations. We investigate a coupled map network as a model motivated by gene regulatory networks and design systems which are robust against phenotypic perturbations…
While training error of most deep neural networks degrades as the depth of the network increases, residual networks appear to be an exception. We show that the main reason for this is the Lyapunov stability of the gradient descent…
Compared with traditional seismic noise attenuation algorithms that depend on signal models and their corresponding prior assumptions, removing noise with a deep neural network is trained based on a large training set, where the inputs are…
We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is…