从实验数据中自动提取低维线性模型，实现复杂系统的全局稳定性分析。
Automated Global Analysis of Experimental Dynamics through Low-Dimensional Linear Embeddings
- 基于时滞嵌入与物理信息自编码器，从原始数据中学习低维坐标表示。
- 可准确预测长期动态，并自动识别复杂不变集，提供实证稳定性保障。
- 适用于物理、气候、工程等领域的非线性系统分析，适合研究复杂动力学的学者。
动力系统理论为理解跨学科的演化现象提供了基础，但将其应用于复杂真实系统仍面临建模困难、非线性及高维性挑战。本文提出一种数据驱动的计算框架，直接从原始实验数据中推导非线性动力系统的低维线性模型。该框架结合时滞嵌入、物理信息深度自编码器和渐进正则化，识别出新型低维坐标表示，揭示多种模拟与先前未研究的实验动力系统中的内在结构。这些新坐标支持长时程精准预测，能自动识别复杂的不变集，并提供经验性的稳定性保证。方法为物理、气候科学与工程等领域复杂动力行为分析提供了新路径，对理解现实世界中的非线性系统具有广泛意义。
原文摘要 · Abstract (English)
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.
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