Exploring nonlinear dynamics and network structures in Kuramoto systems using machine learning approaches

Je Ung Song; Kwangjong Choi; Soo Min Oh; B Kahng

doi:10.1063/5.0153229

Exploring nonlinear dynamics and network structures in Kuramoto systems using machine learning approaches

Chaos. 2023 Jul 1;33(7):073148. doi: 10.1063/5.0153229.

Authors

Je Ung Song¹, Kwangjong Choi¹, Soo Min Oh^{2

3}, B Kahng⁴

Affiliations

¹ CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea.
² Wireless Information and Network Sciences Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
³ Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
⁴ Center for Complex Systems and KI for Grid Modernization, Korea Institute of Energy Technology, Naju 58217, Korea.

PMID: 37486666
DOI: 10.1063/5.0153229

Abstract

Recent advances in machine learning (ML) have facilitated its application to a wide range of systems, from complex to quantum. Reservoir computing algorithms have proven particularly effective for studying nonlinear dynamical systems that exhibit collective behaviors, such as synchronizations and chaotic phenomena, some of which still remain unclear. Here, we apply ML approaches to the Kuramoto model to address several intriguing problems, including identifying the transition point and criticality of a hybrid synchronization transition, predicting future chaotic behaviors, and understanding network structures from chaotic patterns. Our proposed method also has further implications, such as inferring the structure of neural networks from electroencephalogram signals. This study, finally, highlights the potential of ML approaches for advancing our understanding of complex systems.