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

by   Nguyen Anh Khoa Doan, et al.

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.


page 1

page 2

page 3

page 4


Physics-Informed Echo State Networks for Chaotic Systems Forecasting

We propose a physics-informed Echo State Network (ESN) to predict the ev...

A Novel Training Algorithm for HMMs with Partial and Noisy Access to the States

This paper proposes a new estimation algorithm for the parameters of an ...

Understanding physics from interconnected data

Metal melting on release after explosion is a physical system far from q...

Phase2vec: Dynamical systems embedding with a physics-informed convolutional network

Dynamical systems are found in innumerable forms across the physical and...

Reconstruction, forecasting, and stability of chaotic dynamics from partial data

The forecasting and computation of the stability of chaotic systems from...

Physics Informed Topology Learning in Networks of Linear Dynamical Systems

Learning influence pathways of a network of dynamically related processe...

Please sign up or login with your details

Forgot password? Click here to reset