Learning Hidden States in a Chaotic System: A Physics-Informed Echo State Network Approach
This work addresses the challenge of hidden state reconstruction in chaotic dynamical systems for researchers in physics and machine learning, representing an incremental extension of existing methods.
The authors tackled the problem of reconstructing unmeasured states in chaotic systems by extending the Physics-Informed Echo State Network (PI-ESN) framework, achieving accurate reconstruction and robustness to noisy data, with the PI-ESN acting as a denoiser.
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.