相关论文: Neural Network Complexity of Chaos and Turbulence
Deep learning provides a versatile suite of methods for extracting structured information from complex datasets, enabling deeper understanding of underlying fluid dynamic phenomena. The field of turbulence modeling, in particular, benefits…
The complexity and the chaos degree can be used to examine the chaotic aspects of not only several nonlinear classical and quantum physical physics but also life sciences. We will construct a model describing the function of brain in the…
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…
The pressure strain correlation plays a critical role in the Reynolds stress transport modelling. Accurate modelling of the pressure strain correlation leads to proper prediction of turbulence stresses and subsequently the other terms of…
In temporal planning, many different temporal network formalisms are used to model real world situations. Each of these formalisms has different features which affect how easy it is to determine whether the underlying network of temporal…
Streamlines, vortex lines and magnetic flux tubes in turbulent fluids and plasmas display a great amount of coiling, twisting and linking, raising the question as to whether their topological complexity (continually created and destroyed by…
While various complexity measures for deep neural networks exist, specifying an appropriate measure capable of predicting and explaining generalization in deep networks has proven challenging. We propose Neural Complexity (NC), a…
The infinite superpositions of random plane waves are known to be threaded with vortex line singularities which form complicated tangles and obey strict topological rules. We observe that within these structures a timelike axis appears to…
A certain complexity threshold is proposed which defines the term `complex network' for RSN, e.g. Kauffman networks with s>=2 - more than two equally probable state variants. Such Kauffman networks are no longer Boolean networks. RSN are…
It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent…
The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. to precondition searching of optimal control policies in…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the…
Deep neural networks have seen enormous success in various real-world applications. Beyond their predictions as point estimates, increasing attention has been focused on quantifying the uncertainty of their predictions. In this review, we…
Chaotic flow is studied in a series of numerical magnetohydrodynamical simulations that use the shearing box formalism. This mimics important features of local accretion disk dynamics. The magnetorotational instability gives rise to flow…
Three measures of clumpiness of complex networks are introduced. The measures quantify how most central nodes of a network are clumped together. The assortativity coefficient defined in a previous study measures a similar characteristic,…
Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the \emph{edge of chaos} which…
Resilience is a system's ability to maintain its function when perturbations and errors occur. Whilst we understand low-dimensional networked systems' behavior well, our understanding of systems consisting of a large number of components is…