用控制输入扩展极限学习机，仅靠少量参数就能复现系统分岔结构。
Trans-Bifurcation Prediction of Dynamics in terms of Extreme Learning Machines with Control Inputs
- 引入控制输入改进极限学习机，提升对动力系统分岔的建模能力
- 仅用少数参数值训练，即可近乎完整复现目标系统的分岔图
- 揭示了模型高效学习的机制，适用于动力系统分析与预测
通过在极限学习机中引入额外的控制输入，我们几乎完全复现了动力系统中的分岔结构。所提出的神经网络系统展现出惊人学习能力：仅需对少数参数值下的瞬态动态进行训练，即可近乎完整再现目标单参数族动力系统的所有分岔结构。此外，我们提出一种机制来解释这一显著的学习能力，并讨论了当前结果与Kim等人所得类似结果之间的关系。
原文摘要 · Abstract (English)
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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