University of Maryland, College Park, Maryland 20742, USA.
Chaos. 2020 Feb;30(2):023123. doi: 10.1063/1.5132766.
We demonstrate the utility of machine learning in the separation of superimposed chaotic signals using a technique called reservoir computing. We assume no knowledge of the dynamical equations that produce the signals and require only training data consisting of finite-time samples of the component signals. We test our method on signals that are formed as linear combinations of signals from two Lorenz systems with different parameters. Comparing our nonlinear method with the optimal linear solution to the separation problem, the Wiener filter, we find that our method significantly outperforms the Wiener filter in all the scenarios we study. Furthermore, this difference is particularly striking when the component signals have similar frequency spectra. Indeed, our method works well when the component frequency spectra are indistinguishable-a case where a Wiener filter performs essentially no separation.
我们展示了机器学习在使用称为储层计算的技术分离叠加混沌信号中的应用。我们假设对产生信号的动力学方程一无所知，只需要由组成信号的有限时间样本组成的训练数据。我们在由来自两个具有不同参数的洛伦兹系统的信号形成的线性组合的信号上测试我们的方法。将我们的非线性方法与分离问题的最优线性解维纳滤波器进行比较，我们发现我们的方法在我们研究的所有情况下都显著优于维纳滤波器。此外，当组成信号具有相似的频谱时，这种差异尤其明显。事实上，当组成信号的频谱无法区分时——维纳滤波器基本上无法进行分离——我们的方法效果很好。
