Learning Hidden States in a Chaotic System: A Physics-Informed Echo State Network Approach

• URL: http://arxiv.org/abs/2001.02982v2
• Date: Tue, 7 Apr 2020 11:56:40 GMT
• Title: Learning Hidden States in a Chaotic System: A Physics-Informed Echo State Network Approach
• Authors: Nguyen Anh Khoa Doan, Wolfgang Polifke, Luca Magri
• Abstract summary: 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. Non-noisy and noisy datasets are considered.
• Score: 5.8010446129208155
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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