الملخص
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.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Wang, W., Wang, Y., Jiang, Z., Xie, S., & Gong, M. (2026). On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability. https://omanscience.com/ar/articles/on-parameters-of-nonlinear-scalar-dynamics-from-video-invariants-calibration-and-identifiability
MLA 9
Wang, Wenjie, et al. "On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability." https://omanscience.com/ar/articles/on-parameters-of-nonlinear-scalar-dynamics-from-video-invariants-calibration-and-identifiability.
شيكاغو (المؤلف–التاريخ)
Wang, Wenjie, Yuanyuan Wang, Zixiang Jiang, Shaoan Xie, and Mingming Gong. 2026. "On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability." https://omanscience.com/ar/articles/on-parameters-of-nonlinear-scalar-dynamics-from-video-invariants-calibration-and-identifiability.
هارفارد
Wang, W., Wang, Y., Jiang, Z., Xie, S. and Gong, M. (2026) 'On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability', Available at: https://omanscience.com/ar/articles/on-parameters-of-nonlinear-scalar-dynamics-from-video-invariants-calibration-and-identifiability.
فانكوفر
Wang W, Wang Y, Jiang Z, Xie S, Gong M. On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability. https://omanscience.com/ar/articles/on-parameters-of-nonlinear-scalar-dynamics-from-video-invariants-calibration-and-identifiability
IEEE
W. Wang, Y. Wang, Z. Jiang, S. Xie, and M. Gong, "On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability," https://omanscience.com/ar/articles/on-parameters-of-nonlinear-scalar-dynamics-from-video-invariants-calibration-and-identifiability.