# Wind on Trees: Testing Physical Grounding in Dynamic 4D Gaussian Splatting

arXiv: https://arxiv.org/abs/2609.17810 · HTML: https://mlsanity.com/paper/2609.17810/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 15 Sep 2026.

## Builds on (most cited first, 13 of 13)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Dynamic 3D Gaussians: Tracking by Persistent Dynamic View Synthesis](https://mlsanity.com/paper/2308.09713/) (2023)
- [PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics](https://mlsanity.com/paper/2311.12198/) (2023)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [gsplat: An Open-Source Library for Gaussian Splatting](https://mlsanity.com/paper/2409.06765/) (2024)
- [PhysDreamer: Physics-Based Interaction with 3D Objects via Video Generation](https://mlsanity.com/paper/2404.13026/) (2024)
- [PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification](https://mlsanity.com/paper/2303.05512/) (2023)
- [Reconstruction and Simulation of Elastic Objects with Spring-Mass 3D Gaussians](https://mlsanity.com/paper/2403.09434/) (2024)
- [OmniPhysGS: 3D Constitutive Gaussians for General Physics-Based Dynamics Generation](https://mlsanity.com/paper/2501.18982/) (2025)
- [Seeing the Wind from a Falling Leaf](https://mlsanity.com/paper/2512.00762/) (2025)
- [DynamicTree: Interactive Real Tree Animation via Sparse Voxel Spectrum](https://mlsanity.com/paper/2510.22213/) (2025)

## Abstract (arXiv)

Monocular reconstruction of wind-driven vegetation is severely underconstrained: motion along the viewing direction is largely unobservable, a moving canopy offers few reliable correspondences, and nearly the entire scene is dynamic, providing little static reference. Directly-learned deformation fields in 4D Gaussian Splatting therefore optimize photometric consistency rather than recover the motion that produced it. We replace that field with a physically parameterized deformation prior: one damped harmonic oscillator per rigid part, driven by the observed wind and integrated by differentiable RK4, supervised photometrically alone. To test whether such a prior is physically grounded rather than merely well fit, we build a controlled synthetic testbed of three procedurally generated trees spanning an order of magnitude in skeleton complexity, whose per-part natural frequency follows from its own geometry and whose damping ratio is a fixed constant, both held out of training. On it, we measure held-out views, temporal extrapolation, zero-shot transfer to unseen wind speeds, and recovery of the physical parameters themselves. The prior costs appearance fidelity on in-distribution views and extrapolates markedly better outside the training window and the training wind, while parameter recovery is far weaker than it first appears: frequency recovery survives an untrained null control on only the sparsest of the three trees, and damping is not recovered at all.