Faculty
Science
Supervisor Name
Lyle Muller
Keywords
non-linear dynamics, chaos, machine learning, echo state networks, reservoir computing, kuramoto model, oscillator networks
Description
An Echo State Network (ESN) with an activation function based on the Kuramoto model (Kuramoto ESN) is implemented, which can successfully predict the logistic map for a non-trivial number of time steps. The reservoir in the prediction stage exhibits binary dynamics when a good prediction is made, but the oscillators in the reservoir display a larger variability in states as the ESN’s prediction becomes worse. Analytical approaches to quantify how the Kuramoto ESN’s dynamics relate to its prediction are explored, as well as how the dynamics of the Kuramoto ESN relate to another widely studied physical model, the Ising model.
Acknowledgements
The authors would like to acknowledge Gabriel Benigno, Dr. Roberto Budzinski, Molly, and the members of the Muller Lab for insightful discussion and mentorship, and for providing a welcoming and exciting atmosphere in which we were able to explore this project. The authors extend a special thank you to Dr. Lyle Muller for all the mentorship, supervision, and expertise provided throughout the summer. This work is supported by the USRI program at Western and the NSERC USRA program.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Document Type
Poster
A Kuramoto Model Approach to Predicting Chaotic Systems with Echo State Networks
An Echo State Network (ESN) with an activation function based on the Kuramoto model (Kuramoto ESN) is implemented, which can successfully predict the logistic map for a non-trivial number of time steps. The reservoir in the prediction stage exhibits binary dynamics when a good prediction is made, but the oscillators in the reservoir display a larger variability in states as the ESN’s prediction becomes worse. Analytical approaches to quantify how the Kuramoto ESN’s dynamics relate to its prediction are explored, as well as how the dynamics of the Kuramoto ESN relate to another widely studied physical model, the Ising model.