Related papers: Neural Network Complexity of Chaos and Turbulence
We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…
Numerical and experimental turbulence simulations are nowadays reaching the size of the so-called big data, thus requiring refined investigative tools for appropriate statistical analyses and data mining. We present a new approach based on…
Turbulent and vortical flows are ubiquitous and their characterization is crucial for the understanding of several natural and industrial processes. Among different techniques to study spatio-temporal flow fields, complex networks represent…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
In this work, several random Boolean networks (RBN) are generated and analyzed from two characteristics: their time evolution diagram and their transition diagram. For this purpose, its randomness is estimated using three measures, of which…
Turbulence is a complex spatial and temporal structure created by the strong non-linear dynamics of fluid flows at high Reynolds numbers. Despite being an ubiquitous phenomenon that has been studied for centuries, a full understanding of…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
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,…
This paper is a personal overview of the efforts over the last half century to understand fluid turbulence in terms of simpler coherent units. The consequences of chaos and the concept of coherence are first reviewed, using examples from…
Natural complex fluid flow systems exhibit turbulent and chaotic behavior that determines their high-level complexity. Chaos has an accurate mathematical definition, while turbulence is a property of fluid flow without an accurate…
The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles can be regarded as a braid whose properties reflect the underlying dynamics. For a…
Turbulence, the ubiquitous and chaotic state of fluid motions, is characterized by strong and statistically non-trivial fluctuations of the velocity field, over a wide range of length- and time-scales, and it can be quantitatively described…
We address the problem of the relative importance of the intrinsic chaos and the external noise in determining the complexity of population dynamics. We use a recently proposed method for studying the complexity of nonlinear random…
The theoretical explanation for deep neural network (DNN) is still an open problem. In this paper DNN is considered as a discrete-time dynamical system due to its layered structure. The complexity provided by the nonlinearity in the…
Predicting the dynamics of turbulent fluid flows has long been a central goal of science and engineering. Yet, even with modern computing technology, accurate simulation of all but the simplest turbulent flow-fields remains impossible: the…
Complex turbulent flow simulations are an integral aspect of the engineering design process. The mainstay of these simulations is represented by eddy viscosity based turbulence models. Eddy viscosity models are computationally cheap due to…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
A network-based analysis of a turbulent channel flow numerically solved at $Re_\tau=180$ is proposed as an innovative perspective for the spatial characterization of the flow field. Two spatial networks corresponding to the streamwise and…
Deep neural networks use multiple layers of functions to map an object represented by an input vector progressively to different representations, and with sufficient training, eventually to a single score for each class that is the output…
A variety of neural networks architectures are being studied to tackle blur in images and videos caused by a non-steady camera and objects being captured. In this paper, we present an overview of these existing networks and perform…