We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need to evaluate the Lyapunov exponent (LE). The neural network has superior performance for short periods with length down to 10 Lyapunov times on which the traditional LE computation is far from converging. We show the robustness of the neural network to varying control parameters, in particular we train with one set of control parameters, and successfully test in a complementary set. Furthermore, we use the neural network to successfully test the dynamics of discrete maps in different dimensions, e.g. the one-dimensional logistic map and a three-dimensional discrete version of the Lorenz system. Our results demonstrate that a convolutional neural network can be used as an excellent chaos indicator.

中文翻译：

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混沌分类的深度学习

我们训练了一个人工神经网络，该网络可以区分二维Chirikov标准图的混沌和规则动力学。我们使用有限长度的轨迹，并将其性能与需要评估Lyapunov指数（LE）的传统数值方法进行比较。该神经网络在短时间内具有卓越的性能，其长度可低至10 Lyapunov倍，传统LE计算远不能收敛。我们展示了神经网络对变化的控制参数的鲁棒性，特别是我们训练了一组控制参数，并在一组互补的条件下成功进行了测试。此外，我们使用神经网络成功地测试了不同维度上离散地图的动力学，例如一维逻辑地图和Lorenz系统的三维离散版本。