Deep Neural Networks (DNNs) have been successfully applied to investigations of numerical dynamics of finite-dimensional nonlinear systems such as ODEs instead of finding numerical solutions to ODEs via the traditional Runge–Kutta method and its variants. To show the advantages of DNNs, in this paper, we demonstrate that the DNNs are more efficient in finding topological horseshoes in chaotic dynamical systems.

中文翻译：

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通过深度神经网络学习拓扑马蹄形

深度神经网络 (DNN) 已成功应用于有限维非线性系统（例如 ODE）的数值动力学研究，而不是通过传统的龙格-库塔方法及其变体寻找 ODE 的数值解。为了展示 DNN 的优势，在本文中，我们证明了 DNN 在寻找混沌动力系统中的拓扑马蹄铁方面更有效。