Ratas Irmantas, Pyragas Kestutis
<a href="https://ror.org/010310r32">Center for Physical Sciences and Technology</a>, LT-10257 Vilnius, Lithuania.
Phys Rev E. 2024 Jun;109(6-1):064215. doi: 10.1103/PhysRevE.109.064215.
Next-generation reservoir computing is a machine-learning approach that has been recently proposed as an effective method for predicting the dynamics of chaotic systems. So far, this approach has been applied mainly under the assumption that all components of the state vector of dynamical systems are observable. Here we study the effectiveness of this method when only a scalar time series is available for observation. As illustrations, we use the time series of Rössler and Lorenz systems, as well as the chaotic time series generated by an electronic circuit. We found that prediction is only effective if the feature vector of a nonlinear autoregression algorithm contains monomials of a sufficiently high degree. Moreover, the prediction can be improved by replacing monomials with Chebyshev polynomials. Next-generation models, built on the basis of partial observations, are suitable not only for short-term forecasting, but are also capable of reproducing the long-term climate of chaotic systems. We demonstrate the reconstruction of the bifurcation diagram of the Rössler system and the return maps of the Lorenz and electronic circuit systems.
下一代储层计算是一种机器学习方法，最近被提出作为预测混沌系统动力学的有效方法。到目前为止，这种方法主要是在动态系统状态向量的所有分量都可观测的假设下应用的。在这里，我们研究当只有一个标量时间序列可供观测时该方法的有效性。作为示例，我们使用了罗斯勒系统和洛伦兹系统的时间序列，以及由电子电路生成的混沌时间序列。我们发现，只有当非线性自回归算法的特征向量包含足够高次的单项式时，预测才有效。此外，用切比雪夫多项式代替单项式可以改进预测。基于部分观测构建的下一代模型不仅适用于短期预测，还能够再现混沌系统的长期气候。我们展示了罗斯勒系统分岔图以及洛伦兹和电子电路系统返回映射的重建。
