Instituto de Física Interdisciplinar y Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.
Chaos. 2019 Nov;29(11):113113. doi: 10.1063/1.5120822.
In real-world dynamical systems, technical limitations may prevent complete access to their dynamical variables. Such a lack of information may cause significant problems, especially when monitoring or controlling the dynamics of the system is required or when decisions need to be taken based on the dynamical state of the system. Cross-predicting the missing data is, therefore, of considerable interest. Here, we use a machine learning algorithm based on reservoir computing to perform cross-prediction of unknown variables of a chaotic dynamical laser system. In particular, we chose a realistic model of an optically injected single-mode semiconductor laser. While the intensity of the laser can often be acquired easily, measuring the phase of the electric field and the carriers in real time, although possible, requires a more demanding experimental scheme. We demonstrate that the dynamics of two of the three dynamical variables describing the state of the laser can be reconstructed accurately from the knowledge of only one variable, if our algorithm has been trained beforehand with all three variables for a limited period of time. We analyze the accuracy of the method depending on the parameters of the laser system and the reservoir. Finally, we test the robustness of the cross-prediction method when adding noise to the time series. The suggested reservoir computing state observer might be used in many applications, including reconstructing time series, recovering lost time series data and testing data encryption security in cryptography based on chaotic synchronization of lasers.
在实际的动力系统中，技术限制可能会导致无法完全获取其动力变量。这种信息的缺乏可能会导致严重的问题，特别是在需要监测或控制系统的动态或需要根据系统的动态状态做出决策时。因此，跨预测缺失数据是非常有意义的。在这里，我们使用基于储层计算的机器学习算法来对混沌动力激光系统的未知变量进行跨预测。具体来说，我们选择了一个现实的光注入单模半导体激光器模型。虽然激光的强度通常很容易获得，但实时测量电场和载流子的相位虽然可能，但需要更苛刻的实验方案。我们证明，如果我们的算法已经预先用所有三个变量进行了有限时间的训练，那么仅从一个变量的知识就可以准确地重建描述激光状态的三个动力变量中的两个。我们根据激光系统和储层的参数来分析该方法的准确性。最后，我们测试了在时间序列中添加噪声时跨预测方法的鲁棒性。所提出的储层计算状态观测器可用于许多应用，包括重建时间序列、恢复丢失的时间序列数据以及测试基于激光混沌同步的密码学中的数据加密安全性。
