Trans-Bifurcation Prediction of Dynamics in terms of Extreme Learning Machines with Control Inputs
This work addresses the challenge of predicting complex dynamics in systems theory, offering a novel neural network approach that is incremental in its extension of existing methods.
The authors tackled the problem of reproducing bifurcation structures in dynamical systems by extending extreme learning machines with control inputs, achieving nearly complete reproduction of the entire bifurcation structure using only a few parameter values from transient dynamics.
By extending the extreme learning machine by additional control inputs, we achieved almost complete reproduction of bifurcation structures of dynamical systems. The learning ability of the proposed neural network system is striking in that the entire structure of the bifurcations of a target one-parameter family of dynamical systems can be nearly reproduced by training on transient dynamics using only a few parameter values. Moreover, we propose a mechanism to explain this remarkable learning ability and discuss the relationship between the present results and similar results obtained by Kim et al.