Examinando por Autor "Valle, David"

Mostrando 1 - 3 de 3

Characterization of Fractal Basins Using Deep Convolutional Neural Networks
(International Journal of Bifurcation and Chaos, 2022-07-12) Valle, David; Wagemakers, Alexandre; Daza, Alvar; Sanjuán, Miguel A.F.
Neural network models have recently demonstrated impressive prediction performance in complex systems where chaos and unpredictability appear. In spite of the research efforts carried out on predicting future trajectories or improving their accuracy compared to numerical methods, not sufficient work has been done on using deep learning techniques in which the unpredictability can be characterized of chaotic systems or give a general view of the global unpredictability of a system. In this work, we propose a novel approach based on deep learning techniques to measure the fractal dimension of the basins of attraction of the Duffing oscillator for a variety of parameters. As a consequence, we provide an algorithm capable of predicting fractal dimension measures as accurately as the box-counting algorithm, but with a computation speed about ten times faster.
Controlling transient chaos in the Lorenz system with machine learning
(Springer, 2025-03-28) Valle, David; Capeáns, Ruben; Wagemakers, Alexandre; Sanjuán, Miguel A. F.
This paper presents a novel approach to sustain transient chaos in the Lorenz system through the estimation of safety functions using a transformer-based model. Unlike classical methods that rely on iterative computations, the proposed model directly predicts safety functions without requiring finetuning or extensive system knowledge. The results demonstrate that this approach effectively maintains chaotic trajectories within the desired phase space region, even in the presence of noise, making it a viable alternative to traditional methods. A detailed comparison of safety functions, safe sets, and their control performance highlights the strengths and trade-offs of the two approaches.
Deep learning-based analysis of basins of attraction
(American Institute of Physics, 2024-03-04) Valle, David; Wagemakers, Alexandre; Sanjuán, Miguel A.F.
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. Conventional methods become computationally demanding when analyzing multiple basins of attraction across different parameters of dynamical systems. Our research presents an innovative approach that employs CNN architectures for this purpose, showcasing their superior performance in comparison to conventional methods. We conduct a comparative analysis of various CNN models, highlighting the effectiveness of our proposed characterization method while acknowledging the validity of prior approaches. The findings not only showcase the potential of CNNs but also emphasize their significance in advancing the exploration of diverse behaviors within dynamical systems.