Identification of Chimera using Machine Learning

Abstract

Chimera state refers to coexistence of coherent and non-coherent phases in identically coupled dynamical units found in various complex dynamical systems. Identification of Chimera, on one hand is essential due to its applicability in various areas including neuroscience, and on other hand is challenging due to its widely varied appearance in different systems and the peculiar nature of its profile. Therefore, a simple yet universal method for its identification remains an open problem. Here, we present a very distinctive approach using machine learning techniques to characterize different dynamical phases and identify the chimera state from given spatial profiles generated using various different models. The experimental results show that the performance of the classification algorithms varies for different dynamical models. The machine learning algorithms, namely random forest, oblique random forest based on tikhonov, parallel-axis split and null space regularization achieved more than $96\% $ accuracy for the Kuramoto model. For the logistic-maps, random forest and tikhonov regularization based oblique random forest showed more than $90\%$ accuracy, and for the Hénon-Map model, random forest, null-space and axis-parallel split regularization based oblique random forest achieved more than $80\%$ accuracy. The oblique random forest with null space regularization achieved consistent performance (more than $83\%$ accuracy) across different dynamical models while the auto-encoder based random vector functional link neural network showed relatively lower performance. This work provides a direction for employing machine learning techniques to identify dynamical patterns arising in coupled non-linear units on large-scale, and for characterizing complex spatio-temporal patterns in real-world systems for various applications.