mlsanityData to 14 Oct 2026

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

arXiv 2606.00115 ↗First posted 27 May 2026cs.CV cs.LG stat.MLcited by 1

On the map: World models → Latent predictive world models

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.

Key facts. Cited by 1 paper 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.

Builds on

24 of 43 references.

Closest ancestors · 1

Same direction, newest first

  1. 2024How Far is Video Generation from World Model: A Physical Law Perspective4 Nov

Other references · 23

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2019Hamiltonian Neural Networkscited by 712
  3. 2020Lagrangian Neural Networkscited by 398
  4. 2020Universal Differential Equations for Scientific Machine Learningcited by 353
  5. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
  6. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 184
  7. 2025Do generative video models understand physical principles?cited by 161
  8. 2019Hamiltonian Generative Networkscited by 137
  9. 2021gradSim: Differentiable simulation for system identification and visuomotor controlcited by 100
  10. 2017Visual Interaction Networkscited by 95
  11. 2019Physics-as-Inverse-Graphics: Unsupervised Physical Parameter Estimation from Videocited by 45
  12. 2021How I failed machine learning in medical imaging -- shortcomings and recommendationscited by 37
11 more
  1. 2022RISP: Rendering-Invariant State Predictor with Differentiable Simulation and Rendering for Cross-Domain Parameter Estimationcited by 29
  2. 2022Neural Implicit Representations for Physical Parameter Inference from a Single Videocited by 19
  3. 2024Learning Physics From Video: Unsupervised Physical Parameter Estimation for Continuous Dynamical Systemscited by 13
  4. 2020Learning to Identify Physical Parameters from Video Using Differentiable Physicscited by 12
  5. 2021Identifiability Analysis of Linear Ordinary Differential Equation Systems with a Single Trajectorycited by 10
  6. 2025MASIV: Toward Material-Agnostic System Identification from Videoscited by 9
  7. 2022Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observationscited by 8
  8. 2023Physics-guided Shape-from-Template: Monocular Video Perception through Neural Surrogate Modelscited by 8
  9. 2023Generator Identification for Linear SDEs with Additive and Multiplicative Noisecited by 7
  10. 2024One-Shot Real-to-Sim via End-to-End Differentiable Simulation and Renderingcited by 6
  11. 2024Identifiability Analysis of Linear ODE Systems with Hidden Confounderscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026What Can Latent World Models Know? Physical Parameter Identifiability in Multimodal Predictive Representationscited by 3

Similar, not cited

Close in wording, no citation either way

  1. 2026Does Physics Live in the Activations? Localizing Physical Quantities in Video Diffusion Models
  2. 2026Interpreting Physics in Video World Models
  3. 2025Evaluating Newtonian Mechanics in Video Generative Models with Real Physical Systems
  4. 2026The Invisible Hand of Physics: When Video Diffusion Models Know More Than They Show
  5. 2026MPMWorlds: Material-Point-Method Simulations for Inferring and Extrapolating Physical Dynamics
  6. 2026PhysRVG: Physics-Aware Unified Reinforcement Learning for Video Generative Models
  7. 2026Correcting a learned physical invariant improves world-model rollouts
  8. 2026PhySimCode: A Benchmark and Evaluation Method for Physics Video to Code Generation