论文标题
在混乱系统中学习隐藏状态：物理信息的回声状态网络方法
Learning Hidden States in a Chaotic System: A Physics-Informed Echo State Network Approach
论文作者
论文摘要
我们扩展了物理信息的回声状态网络（PI-ESN）框架，以重建混乱系统中未测量状态（隐藏状态）的演变。通过使用（i）数据对PI-ESN进行训练，该数据不包含有关未测量状态的信息，以及（ii）原型混沌动力学系统的物理方程。考虑了非噪声和嘈杂的数据集。首先，证明PI-ESN可以准确地重建未衡量的状态。其次，对嘈杂数据的重建表明重建是可靠的，这意味着PI-ESN充当了DeNoiser。本文为利用物理知识与机器学习之间的协同作用开辟了新的可能性，以增强混乱的动力学系统中未满足状态的重建和预测。
We extend the Physics-Informed Echo State Network (PI-ESN) framework to reconstruct the evolution of an unmeasured state (hidden state) in a chaotic system. The PI-ESN is trained by using (i) data, which contains no information on the unmeasured state, and (ii) the physical equations of a prototypical chaotic dynamical system. Non-noisy and noisy datasets are considered. First, it is shown that the PI-ESN can accurately reconstruct the unmeasured state. Second, the reconstruction is shown to be robust with respect to noisy data, which means that the PI-ESN acts as a denoiser. This paper opens up new possibilities for leveraging the synergy between physical knowledge and machine learning to enhance the reconstruction and prediction of unmeasured states in chaotic dynamical systems.
