对部分观察到的动态系统的回声状态变量网络预测地平线
Ajit Mahata1, Reetish Padhi1, Amit Apte1,2
1Department of Data Science, Indian Institute of Science Education and Research, IISER Pune 411008, India.
Physical review. E
|January 20, 2024
概括
反响状态网络 (ESN) 可以通过部分观测预测动态系统. 这些网络有效地学习系统动态,即使有杂的数据,作为替代模型.
科学领域:
- 动态系统和控制理论.
- 机器学习用于科学建模
- 非线性动力学是一种非线性动力学.
背景情况:
- 动态系统分析通常需要完整的状态信息,这在现实应用中经常是不可用的.
- 部分状态观测在准确建模和预测系统行为方面构成了重大挑战.
研究的目的:
- 调查回声状态网络 (ESN) 对于模拟具有部分状态观测的动态系统的有效性.
- 用模拟和实验数据评估ESN的预测能力和长期学习动态.
主要方法:
- 使用一个回声状态网络 (ESN) 框架,包含部分状态输入和部分或完全状态输出.
- 将ESN方法应用于洛伦茨系统和丘亚振荡器,包括数值模拟和实验推导的数据.
- 分析了预测地平线,它们的可变性,并使用统计指标比较了长期动态.
主要成果:
- 在研究的系统中,ESN显示出对短期预测 (高达几次Lyapunov) 的能力.
- 预测地平线表现出高度依赖初始条件的变化,并详细探索了这种分布.
- ESN有效地学习了系统动态,即使在杂的数据上训练,也表现出与原始系统相似的长期行为.
结论:
- 作为模拟复杂动态系统的具有成本效益的替代模型,ESN具有显著的潜力,特别是在缺乏完整状态观测的情况下.
- 该框架对杂的输入数据具有稳定性,提高了其在现实场景中的实际适用性.
- 对初始条件效应的进一步研究可以完善ESN的预测准确性和地平线估计.
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