预测来自不完整输入的混乱动态,通过 (D+1) 维输入和输出 (D+1) 维的容器计算
Lufa Shi1, Youfang Yan1, Hengtong Wang1
1School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China.
Physical review. E
|June 17, 2023
概括
这项研究引入了一种新的储计算 (RC) 方法,用于从不完整的过去数据中预测复杂系统动态. 增强的RC方法成功地预测未来的状态,即使缺少信息,提高预测的准确性和时间.
科学领域:
- 复杂的系统复杂的系统.
- 机器学习 机器学习
- 非线性动力学是一种非线性动力学.
背景情况:
- 使用机器学习预测复杂的非线性动态具有挑战性,尤其是在不完整的历史数据的情况下.
- 传统的水库计算 (RC) 通常需要完整的过去观测,限制其在缺少数据的现实世界场景中的应用.
研究的目的:
- 提出和验证一个修改后的储计算 (RC) 方案,能够从不完整的时间序列数据中预测未来的系统演变.
- 增强RC的预测能力,用于在输入轨迹中随机删除状态的系统.
主要方法:
- 引入了一个使用 (D+1) 维输入输出向量,并与状态向量一起结合一个时间间隔维度的储计算 (RC) 方案.
- 应用了增强的RC方法来预测后勤地图的未来演变,洛伦茨,罗斯勒和库拉莫托-西瓦辛斯基系统缺少数据.
- 分析了数据丢失率对有效预测时间 (VPT) 的影响,并研究了系统复杂性和可预测性之间的关系.
主要成果:
- 拟议的RC方案成功预测了缺乏动态轨迹数据的系统的未来状态.
- 通过较低的数据丢失率 (θ) 实现了更长的有效预测时间 (VPT).
- 观察到混沌吸引物的完美重建,证明了该方法的有效性.
结论:
- (D+1) 维的RC方案是一个强大的概括,有效地处理不完整和不规则的时间输入数据.
- 与传统的RC相比,这种方法提供了优越的多步预测能力,而不会改变核心架构.
- 可预测性与动态系统的复杂性密切相关,更复杂的系统会带来更大的预测挑战.
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