Predicting bursting in a complete graph of mixed population through reservoir computing

Abstract

We report our investigation and success story, to an extent, on the prediction of spiking and bursting dynamics in globally coupled networks, using echo state network/reservoir computing-based learning procedure. Two exemplary dynamical models, Josephson junctions and Hindmarsh-Rose neurons, are used to construct two separate networks and thereby illustrate the efficacy of our strategy. In the absence of coupling, the networks consist of mixed populations in which few nodes are oscillatory (self-sustained spiking) and the rest of the nodes maintain a quiescent state. When single-input data from one oscillatory node of a network (under stronger interactions between the nodes) is used for learning, the ESN is able to predict the key dynamical features (spiking and bursting) of the other nodes. In comparison, the machine performs with improved predictions if it is fed with two inputs: one from the oscillatory population and another from an excitable population. The machine's leaking parameter plays a crucial role, which can be tuned appropriately to enhance prediction. Furthermore, a cluster synchronization in the mixed population is confirmed from the machine-generated output signals. Our work is expected to be useful as a burst predictor.

Predicting the data structure prior to extreme events from passive observables using echo state network

“…ESN is a simple version of recurrent neural networks [39] that has been used extensively to predict complex signals ranging from time series generated from chaotic model, stock-price data to tune hyperparameter [40][41][42][43][44][45][46][47][48][49][50]. Recently, it has been shown that ESN can efficiently capture the onset of generalized synchronization [51-55], quenching of oscillation [56,57], detect collective bursting in neuron populations [58], and predict epidemic spreading [59]. ESN has been shown to have great potential in handling multiple inputs of temporal data, and ability to trace the relation between them [52,58,60].…”

“…Recently, it has been shown that ESN can efficiently capture the onset of generalized synchronization [51-55], quenching of oscillation [56,57], detect collective bursting in neuron populations [58], and predict epidemic spreading [59]. ESN has been shown to have great potential in handling multiple inputs of temporal data, and ability to trace the relation between them [52,58,60]. Due to its simple and computationally effective character and its suitability for dynamical systems, we use ESN for our study.…”

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

“…Each burst is followed by a quiescence state before the next burst occurs and it can be periodic or chaotic. In a recent study [64], it has been revealed that for a mixed population of coupled oscillators, ESN needs at least one time series data from each group to get a satisfactory spiking and bursting prediction as well as predicting the onset of generalized synchronization. However, this prediction of bursting dynamics by ESN was limited to a complete (uncorrelated) graph and the original as well as machine generated profile of the bursts were periodic.…”