Title: Physics from Video: Identifiability of Time-Invariant Second-Order ODEs under Minimal Trajectory Conditions

Abstract

Reconciling visual fidelity with physical comprehension remains a fundamental hurdle for video-driven world models. This study investigates the structural identifiability of continuous-time physical laws derived directly from raw pixel data, specifically examining whether an encoder-only architecture can singularly determine the parameters of second-order linear ordinary differential equations (ODEs). We demonstrate that a level-set slope-coverage condition guarantees the learned latent space is locally affine to the actual physical state, thereby facilitating precise parameter recovery. Our theoretical framework offers the initial characterization of the minimum data necessary across various damping regimes, revealing that while underdamped systems can be identified from a solitary video clip, other regimes necessitate three distinct trajectories. To mitigate latent collapse and stabilize the decoder-free objective, we propose a variance-floor regularizer. Empirical evaluations on both synthetic and real-world datasets confirm that this method reliably estimates interpretable physical constants from video input. By eliminating the computational burden of pixel reconstruction, our approach ensures both physical accuracy and transparency. The code is accessible at https://github.com/wenjiewang3/PhysicsFromVideo.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC