发表机构
University of Melbourne; Mohamed bin Zayed University of Artificial Intelligence; Carnegie Mellon University（墨尔本大学; 穆罕默德·本·扎耶德人工智能大学; 卡内基梅隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对视频中非线性标量二阶ODE的参数可辨识性，提出按速度依赖分类的理论，揭示唯一可辨识、不变组合或需标定的条件，并实验验证。
AI 中文摘要
从视频中进行物理参数估计旨在从像素观测中恢复已知动力学方程族的参数。现有针对该场景的可辨识性理论集中于线性时不变（LTI）二阶系统，对于非线性标量动力学可辨识什么的问题仍未解决。我们针对非线性标量二阶常微分方程发展了一套可辨识性理论，其组织方式基于速度依赖如何与学习到的状态坐标变换相互作用。在共享的非塌缩状态映射和明确的同状态速度覆盖条件下，我们证明参数可辨识性取决于ODE族：某些参数是唯一可辨识的，而在其他族中，只有不变参数组合可辨识，或需要外部物理标定。对于速度至多线性的定律，兼容性强制仿射坐标对齐，从而产生显式的参数关系、不变量和标定条件。当坐标曲率可与声明的速度依赖分离时，该仿射结论扩展到更广泛的有限速度特征族。对于允许平方速度项的族，非线性坐标模糊性可能仍然存在；基于定律的归一化反而能在规范定律之间实现仿射比较。在合成系统以及真实摆和自由落体视频上的实验支持了预测的参数关系、覆盖效应和标定要求。
英文摘要
Physical parameter estimation from video aims to recover the parameters of a known family of governing dynamical equations from pixel observations. Existing identifiability theory for this setting has focused on linear time-invariant (LTI) second-order systems, leaving open what can be identified for nonlinear scalar dynamics. We develop an identifiability theory for nonlinear scalar second-order ODEs, organized by how their velocity dependence interacts with changes of the learned state coordinate. Under a shared non-collapsed state map and explicit same-state velocity-coverage conditions, we show that parameter identifiability depends on the ODE family: some parameters are uniquely identifiable, while in other families only invariant parameter combinations are identifiable or external physical calibration is required. For laws that are at most linear in velocity, compatibility forces affine coordinate alignment, yielding explicit parameter relations, invariants, and calibration conditions. This affine conclusion extends to broader finite velocity-feature families when coordinate curvature can be separated from the declared velocity dependence. For families admitting a squared-velocity term, nonlinear coordinate ambiguity can remain; a law-derived normalization instead enables affine comparison between canonical laws. Experiments on synthetic systems and real pendulum and free-fall videos support the predicted parameter relations, coverage effects, and calibration requirements.
