从视频中自动发现系统动力学的低维可操作表示。
Automated Discovery of Operable Dynamics from Videos
- 直接从视频提取紧凑状态变量和可微向量场。
- 能准确识别稳定平衡点与混沌行为。
- 适合自动化科学发现与物理建模研究者。
动力系统是科学发现的基础，传统上依赖预定义的状态变量（如角度和角速度）和微分方程（如单摆运动方程）。我们提出一种框架，无需领域先验知识，直接从视频中自动发现系统动力学的低维、可操作表示，包括一组保持系统平滑性的紧凑状态变量和一个可微向量场。通过定量与定性分析多种动力系统，验证了该方法的有效性：能够识别稳定平衡点、预测自然频率，并检测混沌与极限环行为。结果表明，这一数据驱动方法在推动自动化科学发现方面具有巨大潜力。
原文摘要 · Abstract (English)
Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum. We introduce a framework that automatically discovers a low-dimensional and operable representation of system dynamics, including a set of compact state variables that preserve the smoothness of the system dynamics and a differentiable vector field, directly from video without requiring prior domain-specific knowledge. The prominence and effectiveness of the proposed approach are demonstrated through both quantitative and qualitative analyses of a range of dynamical systems, including the identification of stable equilibria, the prediction of natural frequencies, and the detection of chaotic and limit cycle behaviors. The results highlight the potential of our data-driven approach to advance automated scientific discovery.
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