Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical modeling, nonlinearity, and high dimensionality. In this work, we introduce a data-driven computational framework to derive low-dimensional linear models for nonlinear dynamical systems directly from raw experimental data. This framework enables global stability analysis through interpretable linear models that capture the underlying system structure. Our approach employs time-delay embedding, physics-informed deep autoencoders, and annealing-based regularization to identify novel low-dimensional coordinate representations, unlocking insights across a variety of simulated and previously unstudied experimental dynamical systems. These new coordinate representations enable accurate long-horizon predictions and automatic identification of intricate invariant sets while providing empirical stability guarantees. Our method offers a promising pathway to analyze complex dynamical behaviors across fields such as physics, climate science, and engineering, with broad implications for understanding nonlinear systems in the real world.

本研究解决了在复杂现实系统中应用动态系统理论所面临的数学建模、非线性和高维度问题。我们提出了一种数据驱动的计算框架，能够直接从原始实验数据中推导出非线性动态系统的低维线性模型，从而实现全局稳定性分析。这种新方法提供了对复杂动态行为的深入理解，具有广泛的应用潜力，特别是在物理、气候科学和工程等领域。

通过低维线性嵌入的实验动态自动化全球分析