Harding S, Leishman Q, Lunceford W, Passey D J, Pool T, Webb B
Mathematics Department, Brigham Young University, Provo, Utah 84602, USA.
Mathematics Department, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA.
Chaos. 2024 Feb 1;34(2). doi: 10.1063/5.0181694.
A reservoir computer is a machine learning model that can be used to predict the future state(s) of time-dependent processes, e.g., dynamical systems. In practice, data in the form of an input-signal are fed into the reservoir. The trained reservoir is then used to predict the future state of this signal. We develop a new method for not only predicting the future dynamics of the input-signal but also the future dynamics starting at an arbitrary initial condition of a system. The systems we consider are the Lorenz, Rossler, and Thomas systems restricted to their attractors. This method, which creates a global forecast, still uses only a single input-signal to train the reservoir but breaks the signal into many smaller windowed signals. We examine how well this windowed method is able to forecast the dynamics of a system starting at an arbitrary point on a system's attractor and compare this to the standard method without windows. We find that the standard method has almost no ability to forecast anything but the original input-signal while the windowed method can capture the dynamics starting at most points on an attractor with significant accuracy.
储层计算机是一种机器学习模型，可用于预测随时间变化的过程（例如动态系统）的未来状态。在实践中，以输入信号形式的数据被输入到储层中。然后，经过训练的储层用于预测该信号的未来状态。我们开发了一种新方法，不仅可以预测输入信号的未来动态，还可以预测从系统的任意初始条件开始的未来动态。我们考虑的系统是限制在其吸引子上的洛伦兹系统、罗斯勒系统和托马斯系统。这种创建全局预测的方法仍然只使用单个输入信号来训练储层，但将信号分解为许多较小的窗口信号。我们研究这种窗口方法能够多好地预测从系统吸引子上的任意点开始的系统动态，并将其与无窗口的标准方法进行比较。我们发现，标准方法几乎没有能力预测除原始输入信号之外的任何东西，而窗口方法可以以显著的精度捕捉从吸引子上大多数点开始的动态。
