标题： 使用深度卷积神经网络表征分形盆地 显示英文标题

标题： Characterization of Fractal Basins Using Deep Convolutional Neural Networks

摘要： 神经网络模型最近在出现混沌和不可预测性的复杂系统中展示了令人印象深刻的预测性能。 尽管已经进行了大量研究以预测未来轨迹或提高其准确性，与数值方法相比，使用深度学习技术来表征混沌系统的不可预测性或提供系统全局不可预测性的总体观点的工作仍不够充分。 在本工作中，我们提出了一种基于深度学习技术的新方法，用于测量杜芬振子在不同参数下的吸引盆地的分形维数。 因此，我们提供了一个算法，能够像传统算法一样准确地预测分形维数，但计算速度大约快十倍。 显示英文摘要

摘要： 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 by using deep learning techniques in which they characterize the unpredictability 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 conventional algorithm, but with a computation speed about ten times faster.