Physics from Video: Identifiability of Time-Invariant Second-Order ODEs under Minimal Trajectory Conditions
Bridging the gap between visual realism and physical understanding is a core challenge for video-based world models. We study the structural identifiability of continuous-time physical laws from raw pixels, focusing on whether an encoder-only pipeline can uniquely recover the parameters of second-order linear ODEs. We prove that a level-set slope-coverage condition ensures the learned latent space is locally affine to the true physical state, enabling exact parameter recovery. Our theory provides the first characterization of minimal data requirements across damping regimes, establishing that underdamped systems are identifiable from a single video clip, whereas other regimes require thre...
| Authors | Yuanyuan Wang, Wenjie Wang, Kun Zhang et al. |
|---|---|
| Primary category | cs.CV |
| Published | 27 May 2026 |
| Last updated at source | 31 July 2026 |
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