# On Parameters of Nonlinear Scalar Dynamics from Video: Invariants, Calibration, and Identifiability

arXiv: https://arxiv.org/abs/2609.38877 · HTML: https://mlsanity.com/paper/2609.38877/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 41 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 4 of 4)

- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Evaluating Newtonian Mechanics in Video Generative Models with Real Physical Systems](https://mlsanity.com/paper/2504.02918/) (2025)
- [Interpreting Physics in Video World Models](https://mlsanity.com/paper/2602.07050/) (2026)
- [Extracting Governing Equations from Latent Dynamics via Multi-View Contrastive Learning](https://mlsanity.com/paper/2606.13260/) (2026)

## Abstract (arXiv)

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.