Predicting slow and fast neuronal dynamics with machine learning

Abstract

In this work, we employ reservoir computing, a recently developed machine learning technique, to predict the time evolution of neuronal activity produced by the Hindmarsh-Rose neuronal model. Our results show accurate short- and long-term predictions for periodic (tonic and bursting) neuronal behaviors, but only short-term accurate predictions for chaotic neuronal states. However, after the accuracy of the short-term predictability deteriorates in the chaotic regime, the predicted output continues to display similarities with the actual neuronal behavior. This is reinforced by a striking resemblance between the bifurcation diagrams of the actual and of the predicted outputs. Error analyses of the reservoir’s performance are consistent with standard results previously obtained.

Using Machine Learning to Anticipate Tipping Points and Extrapolate to Post-Tipping Dynamics of Non-Stationary Dynamical Systems

“…Machine learning has been widely applied to the problem of determining both the short-term future state evolution [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the long-term "climate" [18][19][20][21] of stationary dynamical systems. In this paper, we use the term "climate" to denote long-term statistical properties of the evolution of a dynamical system.…”

Learning Coupled Oscillators System with Reservoir Computing

“…Recently, some model-free prediction methods have been proposed for the synchronization of chaotic systems using reservoir computing methods [10][11][12][13]. The state evolution of chaotic systems is predicted by RC [14][15][16][17][18][19]. The idea and principle of using reservoir computing for model-free systems are first proposed about two decades ago [10,19].…”

Learning Hamiltonian dynamics by reservoir computer

“…Model-free prediction of chaotic dynamical systems using machine learning approaches has received broad research interest in recent years [1][2][3][4][5]. In particular, a technique knowing as reservoir computer (RC) has been widely adopted in literature for predicting the state evolution of chaotic systems [6][7][8][9][10][11][12][13][14][15][16]. From the perspective of dynamical systems, RC can be regarded as a complex network of coupled dynamical elements, which, driven by the input data, generates the output data through a readout function.…”

“…This ability, knowing as climate replication, suggests that it is the intrinsic dynamics of the chaotic system * Email address: wangxg@snnu.edu.cn that RC essentially learns from the data, instead of the mathematical expressions describing the time series. Exploiting this ability, model-free techniques have been proposed in recent years to predict the bifurcations in nonlinear dynamical systems, e.g., reproducing the bifurcation diagram of classical chaotic systems [13,14], anticipating the critical points of system collapse [19], predicting the critical coupling for synchronization [20], etc. Another property revealed recently in exploiting RC is that knowledge can be transferred between different dynamical systems, namely the ability of transfer learning [21,22].…”