The reservoir’s perspective on generalized synchronization

Abstract

We employ reservoir computing for a reconstruction task in coupled chaotic systems, across a range of dynamical relationships including generalized synchronization. For a drive-response setup, a temporal representation of the synchronized state is discussed as an alternative to the known instantaneous form. The reservoir has access to both representations through its fading memory property, each with advantages in different dynamical regimes. We also extract signatures of the maximal conditional Lyapunov exponent in the performance of variations of the reservoir topology. Moreover, the reservoir model reproduces different levels of consistency where there is no synchronization. In a bidirectional coupling setup, high reconstruction accuracy is achieved despite poor observability and independent of generalized synchronization.

Optimizing Reservoir Computers for Signal Classification

“…Several groups have been using theory to better understand reservoir computers; in Hart et al (2020), the authors show that there is a positive probability that a reservoir computer can be an embedding of the driving system, and therefore can predict the future of the driving system within an arbitrary tolerance. Lymburn et al (2019) study the relation between generalized synchronization and reconstruction accuracy, while Herteux and Räth examine how the symmetry of the activation function affects reservoir computer performance (Herteux and Rath, 2020).…”

Optimized ensemble deep learning framework for scalable forecasting of dynamics containing extreme events

“…In this context, reservoir computing (RC) [29][30][31], a version of recurrent neural network model, is effective for inference of unmeasured variables in chaotic systems using values of a known variable [32], forecasting dynamics of chaotic oscillators [33,34], predicting the evolution of the phase of chaotic dynamics [35], and prediction of critical transition in dynamical systems [36]. Also, RC is used to detect synchronization [37][38][39], spiking-bursting phenomena [40], inferring network links [41] in coupled systems. Apart from the RC, researchers have also applied different architectures of artificial neural networks such as feed-forward neural network (FFNN) [42,43], long-short term memory (LSTM) [44][45][46] for different purposes such as detecting phase transition in complex network [47], and functional connectivity in coupled systems [48], forecasting of complex dynamics [49].…”

Role of assortativity in predicting burst synchronization using echo state network

“…[43][44][45][46][47] , those can be efficiently identified and extracted with the machine learning tools. The critical parameter for the amplitude death [48], and the onset of generalized synchronization can easily be captured using ESN [49,50] based approach. First-order and second-order phase transition of a system of non-identical oscillators can be predicted through ESN as well [51].…”