Related papers: Characterization of Fractal Basins Using Deep Conv…
This research addresses the challenge of characterizing the complexity and unpredictability of basins within various dynamical systems. The main focus is on demonstrating the efficiency of convolutional neural networks (CNNs) in this field.…
The fractal dimension provides a statistical index of object complexity by studying how the pattern changes with the measuring scale. Although useful in several classification tasks, the fractal dimension is under-explored in deep learning…
In this article, we present a novel box-covering algorithm for analyzing the fractal properties of complex networks. Unlike traditional algorithms that impose a predetermined box size, our approach assigns nodes to boxes identified by their…
Fundamental limits to predictability are central to our understanding of many physical and computational systems. Here we show that, despite its remarkable capabilities, deep learning exhibits such fundamental limits rooted in the fractal,…
In dynamical systems, basins of attraction connect a given set of initial conditions in phase space to their asymptotic states. The basin entropy and related tools quantify the unpredictability in the final state of a system when there is…
This paper describes a study based on computational fluid dynamics (CFD) and deep neural networks that focusing on predicting the flow field in differently distorted U-shaped pipes. The main motivation of this work was to get an insight…
Developing a robust generalization measure for the performance of machine learning models is an important and challenging task. A lot of recent research in the area focuses on the model decision boundary when predicting generalization. In…
Power systems dominated by renewable energy encounter frequently large, random disturbances, and a critical challenge faced in power-system management is how to anticipate accurately whether the perturbed systems will return to the…
We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…
Fractal geometry, defined by self-similar patterns across scales, is crucial for understanding natural structures. This work addresses the fractal inverse problem, which involves extracting fractal codes from images to explain these…
Recent efforts have shown machine learning to be useful for the prediction of nonlinear fluid dynamics. Predictive accuracy is often a central motivation for employing neural networks, but the pattern recognition central to the network…
In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…
Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…
The study of chaos has long relied on computationally intensive methods to quantify unpredictability and design control strategies. Recent advances in machine learning, from convolutional neural networks to transformer architectures,…
In many real complex networks, the fractal and self-similarity properties have been found. The fractal dimension is a useful method to describe fractal property of complex networks. Fractal analysis is inadequate if only taking one fractal…
This paper introduces a scale-invariant methodology employing \textit{Fractal Geometry} to analyze and explain the nonlinear dynamics of complex connectionist systems. By leveraging architectural self-similarity in Deep Neural Networks…
Disobeying the classical wisdom of statistical learning theory, modern deep neural networks generalize well even though they typically contain millions of parameters. Recently, it has been shown that the trajectories of iterative…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
In this study, we propose a multi branched network approach to predict the dynamics of a physics attractor characterized by intricate and chaotic behavior. We introduce a unique neural network architecture comprised of Radial Basis Function…
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…