论文标题
混乱分类的深度学习
Deep Learning of Chaos Classification
论文作者
论文摘要
我们训练一个人工神经网络，该神经网络区分了二维Chirikov标准图的混乱和常规动力学。我们使用有限的长度轨迹，并将性能与需要评估Lyapunov指数的传统数值方法进行比较。神经网络在短时间内具有出色的性能，长度降至10个Lyapunov时间，传统的Lyapunov指数计算远非融合。我们显示了神经网络对改变控制参数的鲁棒性，特别是我们使用一组控制参数训练，并在互补集中成功测试。此外，我们使用神经网络在不同维度（例如洛伦兹系统的一维逻辑图和三维离散版本。我们的结果表明，卷积神经网络可以用作出色的混乱指标。
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. The neural network has superior performance for short periods with length down to 10 Lyapunov times on which the traditional Lyapunov exponent 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.
