Related papers: Deep Learning of Chaos Classification
Deep neural networks (DNNs) are vulnerable to subtle adversarial perturbations applied to the input. These adversarial perturbations, though imperceptible, can easily mislead the DNN. In this work, we take a control theoretic approach to…
We introduce techniques for exploring the functionality of a neural network and extracting simple, human-readable approximations to its performance. By performing gradient ascent on the input space of the network, we are able to produce…
In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov…
Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons, lasers, chemical reactions, arrhythmic cardiac tissue, and spontaneously bursting neuronal networks. An underlying…
Deep learning has had a far reaching impact in robotics. Specifically, deep reinforcement learning algorithms have been highly effective in synthesizing neural-network controllers for a wide range of tasks. However, despite this empirical…
This paper reveals a novel numerical method, the sequential test, which approves chaos through sequences of numbers observations. The method alights alongside the Lyapunov exponent and bifurcation diagram test. Explicitly elucidation of the…
Texture classification is a pivotal task in computer vision, presenting unique challenges due to high inter-class similarity and the sensitivity of structural patterns to scale and illumination changes. While Convolutional Neural Networks…
In this study, we address the problem of chaotic synchronization over a noisy channel by introducing a novel Deep Chaos Synchronization (DCS) system using a Convolutional Neural Network (CNN). Conventional Deep Learning (DL) based…
This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…
In this paper, we study instances of complex neural networks, i.e. neural netwo rks with complex topologies. We use Self-Organizing Map neural networks whose n eighbourhood relationships are defined by a complex network, to classify handwr…
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…
The objective of this paper is to enhance the optimization process for neural networks by developing a dynamic learning rate algorithm that effectively integrates exponential decay and advanced anti-overfitting strategies. Our primary…
Deep neural networks tend to underestimate uncertainty and produce overly confident predictions. Recently proposed solutions, such as MC Dropout and SDENet, require complex training and/or auxiliary out-of-distribution data. We propose a…
Recently an algorithm, was discovered, which separates points in n-dimension by planes in such a manner that no two points are left un-separated by at least one plane{[}1-3{]}. By using this new algorithm we show that there are two ways of…
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…
Many different classification tasks need to manage structured data, which are usually modeled as graphs. Moreover, these graphs can be dynamic, meaning that the vertices/edges of each graph may change during time. Our goal is to jointly…
Reconstructing network dynamics from data is crucial for predicting the changes in the dynamics of complex systems such as neuron networks; however, previous research has shown that the reconstruction is possible under strong constraints…
Depending on initial conditions, individual finite time trajectories of dynamical systems can have very different chaotic properties. Here we present a numerical method to identify trajectories with atypical chaoticity, pathways that are…
Neural networks have become a widely adopted tool for tackling a variety of problems in machine learning and artificial intelligence. In this contribution we use the mathematical framework of local stability analysis to gain a deeper…
The fields of neural computation and artificial neural networks have developed much in the last decades. Most of the works in these fields focus on implementing and/or learning discrete functions or behavior. However, technical, physical,…