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

arXiv: https://arxiv.org/abs/2606.00115 · HTML: https://mlsanity.com/paper/2606.00115/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Latent predictive world models, one of 11 directions in World models.
- Builds on 24 of its 43 references that are in the map.
- First posted on arXiv 27 May 2026.

## Placed in

- World models / [Latent predictive world models](https://mlsanity.com/wm/latent-predictive-world-models/)

## Builds on (most cited first, 24 of 24)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [How Far is Video Generation from World Model: A Physical Law Perspective](https://mlsanity.com/paper/2411.02385/) (2024)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Do generative video models understand physical principles?](https://mlsanity.com/paper/2501.09038/) (2025)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [Visual Interaction Networks](https://mlsanity.com/paper/1706.01433/) (2017)
- [Physics-as-Inverse-Graphics: Unsupervised Physical Parameter Estimation from Video](https://mlsanity.com/paper/1905.11169/) (2019)
- [How I failed machine learning in medical imaging -- shortcomings and recommendations](https://mlsanity.com/paper/2103.10292/) (2021)
- [RISP: Rendering-Invariant State Predictor with Differentiable Simulation and Rendering for Cross-Domain Parameter Estimation](https://mlsanity.com/paper/2205.05678/) (2022)
- [Neural Implicit Representations for Physical Parameter Inference from a Single Video](https://mlsanity.com/paper/2204.14030/) (2022)
- [Learning Physics From Video: Unsupervised Physical Parameter Estimation for Continuous Dynamical Systems](https://mlsanity.com/paper/2410.01376/) (2024)
- [Learning to Identify Physical Parameters from Video Using Differentiable Physics](https://mlsanity.com/paper/2009.08292/) (2020)
- [Identifiability Analysis of Linear Ordinary Differential Equation Systems with a Single Trajectory](https://mlsanity.com/paper/2103.05660/) (2021)
- [MASIV: Toward Material-Agnostic System Identification from Videos](https://mlsanity.com/paper/2508.01112/) (2025)
- [Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations](https://mlsanity.com/paper/2210.05955/) (2022)
- [Physics-guided Shape-from-Template: Monocular Video Perception through Neural Surrogate Models](https://mlsanity.com/paper/2311.12796/) (2023)
- [Generator Identification for Linear SDEs with Additive and Multiplicative Noise](https://mlsanity.com/paper/2310.19491/) (2023)
- [One-Shot Real-to-Sim via End-to-End Differentiable Simulation and Rendering](https://mlsanity.com/paper/2412.00259/) (2024)
- [Identifiability Analysis of Linear ODE Systems with Hidden Confounders](https://mlsanity.com/paper/2410.21917/) (2024)

## Built on by (most cited first, 1 of 1)

- [What Can Latent World Models Know? Physical Parameter Identifiability in Multimodal Predictive Representations](https://mlsanity.com/paper/2607.27017/) (2026)

## Abstract (arXiv)

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 three diverse trajectories. We further introduce a variance-floor regularizer to stabilize the decoder-free objective and prevent latent collapse. Validated on synthetic and real-world data, our approach demonstrates that interpretable physical constants can be reliably estimated from video without the need for compute-intensive pixel reconstruction, ensuring both physical correctness and transparency. Code is available at https://github.com/wenjiewang3/PhysicsFromVideo.