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象征性的扩展动态模式分解
Connor Kennedy1, John Kaushagen1, Hong-Kun Zhang1
1Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, Massachusetts 01003, USA.
Chaos (Woodbury, N.Y.)
|September 30, 2024
概括
本研究介绍了一种新的扩展动态模式分解 (EDMD) 方法,使用混乱系统的符号表示. 新的方法提高了库普曼运营商的估计和预测准确度.
科学领域:
- 动态系统理论 动态系统理论
- 数据驱动的科学发现.
- 数字分析 数字分析
背景情况:
- 扩展动态模式分解 (EDMD) 是通过估计库普曼运算符来分析复杂动态系统的强大工具.
- 在EDMD的一个关键挑战是选择一个有效的可观测词典.
- 符号表示提供了一种结构化的方法来定义某些动态系统的可观察值.
研究的目的:
- 开发一种新的EDMD方法,适用于具有符号表示的系统.
- 使用符号动态构建一个有效的EDMD字典.
- 分析拟议方法的理论趋同和实际估计界限.
主要方法:
- 从系统状态空间的生成分区中得出的"圆柱体集"的指标构建字典.
- 将EDMD应用于具有已知或可估计生成分区的混乱动态系统.
- 证明了对投影和EDMD估计 (Km) 的强烈运算符拓趋同.
主要成果:
- 证明了对投影和EDMD估计 (Km) 的强烈运营者拓趋同.
- 建立了用于投影和千米的实际有限步骤估计边界.
- 成功地将该方法应用于二度和物流地图,用于自身光谱估计和预测.
结论:
- 拟议的EDMD方法有效地利用符号表示来构建一个最佳的字典.
- 该方法在理论上提供了对收的保证,并为估计准确性的实际限制.
- 这种方法增强了EDMD分析和预测混乱动态系统的能力.
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