准周期驱动动力学的数据驱动发现
Data-driven discovery of quasiperiodically driven dynamics
AI总结：
提出完全数据驱动的框架，结合核谐波分析、核插值和Koopman算子理论，从时间序列中识别并重建准周期驱动动力系统的驱动源与被驱动非线性动力学，在三个真实案例中实现准确重建与频率识别。
摘要：
如果在分析时间序列时假设其由潜在的动力系统生成，则可获得许多新视角。例如，数据的统计特性可与动力学的测度论方面相关联，并可尝试重建动力学本身。潜在动力学可表示自然现象或物理系统，其中时间序列代表一系列测量值。本文提出一个完全数据驱动的框架，用于从生成的时间序列中识别和建模准周期驱动的动力系统（Q.P.D.）。Q.P.D.是一类特殊的系统，由具有多个基频的周期源驱动。这类系统在自然界中大量存在，如天文学和交通流。我们的框架将动力学重建为两个组件：具有生成频率的驱动准周期源，以及被驱动的非线性动力学。我们结合使用了基于核的谐波分析、基于核的插值技术和Koopman算子理论。该框架为三个真实世界案例研究提供了准确的重建和频率识别。
英文摘要：
The analysis of a timeseries can provide many new perspectives if it is accompanied by the assumption that the timeseries is generated from an underlying dynamical system. For example, statistical properties of the data can be related to measure theoretic aspects of the dynamics, and one can try to recreate the dynamics itself. The underlying dynamics could represent a natural phenomenon or a physical system, where the timeseries represents a sequence of measurements. In this paper, we present a completely data-driven framework to identify and model quasiperiodically driven dynamical systems (Q.P.D.) from the timeseries it generates. Q.P.D. are a special class of systems that are driven by a periodic source with multiple base frequencies. Such systems abound in nature, e.g., astronomy and traffic flow. Our framework reconstructs the dynamics into two components - the driving quasiperiodic source with generating frequencies; and the driven nonlinear dynamics. We make a combined use of a kernel-based harmonic analysis, kernel-based interpolation technique, and Koopman operator theory. Our framework provides accurate reconstructions and frequency identification for three real-world case studies.
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