提高数据驱动的动态建模与自动区分的预测能力:库普曼和神经ODE方法
C Ricardo Constante-Amores1, Alec J Linot2, Michael D Graham1
1Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
Chaos (Woodbury, N.Y.)
|April 4, 2024
概括
一种新方法改进了库普曼运算符近似用于复杂系统动态预测. 这种数据驱动的方法优于用词典学习 (EDMD-DL) 进行扩展动态模式分解,并提供与状态空间模型相比具有竞争力的结果.
科学领域:
- 动态系统和控制理论.
- 机器学习用于科学发现
- 计算物理与工程 计算物理与工程
背景情况:
- 预测复杂的动态系统的时间演变在科学和工程方面至关重要.
- 数据驱动的库普曼运算子近似为分析非线性动态提供了强大的框架.
- 扩展动态模式分解与字典学习 (EDMD-DL) 是一个突出的但可以改进的方法.
研究的目的:
- 开发一种修改后的EDMD-DL方法,同时优化可观测的词典和库普曼运算子近似.
- 对各种基于库普曼和状态空间的方法进行评估,以评估拟议方法的性能.
- 评估各种动态系统的预测准确性,包括具有复杂吸引力的ODEs和PDEs.
主要方法:
- 引入了一种新的EDMD-DL变体,利用自动差异化来通过伪反向实现基于梯度的优化.
- 将拟议的方法与"纯粹的"库普曼方法 (可观测空间中的时间整合) 相比较.
- 评估了交替状态可观测空间库普曼方法和神经普通微分方程 (状态空间) 方法.
主要成果:
- 拟议的修改EDMD-DL框架显著优于标准EDMD-DL.
- 状态空间方法表现出比"纯粹"库普曼方法更好的预测性能.
- 交替状态可观测空间库普曼方法实现了与状态空间方法相比的预测准确性.
结论:
- 开发的数据驱动框架增强了对复杂系统动态的库普曼操作员近似度.
- 该研究强调了不同库普曼运算符实现和状态空间模型之间的权衡.
- 这项工作为预测复杂动态系统的时间演变提供了更强大,更准确的工具.
相关概念视频
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