Trans-Bifurcation Prediction of Dynamics in terms of Extreme Learning Machines with Control Inputs

Satoru Tadokoro; Akihiro Yamaguchi; Takao Namiki; Ichiro Tsuda

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arXiv · 2410.13289

Trans-Bifurcation Prediction of Dynamics in terms of Extreme Learning Machines with Control Inputs

Satoru Tadokoro·Akihiro Yamaguchi·Takao Namiki·Ichiro Tsuda

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Abstract

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.

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Satoru Tadokoro, Akihiro Yamaguchi, Takao Namiki, Ichiro Tsuda. 2024-10-17. Trans-Bifurcation Prediction of Dynamics in terms of Extreme Learning Machines with Control Inputs. https://arxiv.org/abs/2410.13289

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