GaussPDE enables dynamic rendering with 3D Gaussian scenes and PDEs
GaussPDE: Graph-Based Partial Differential Equation-Driven Rendering for 3D Gaussian Splatting
Computer Vision and Pattern Recognition
Summary
Rendering 3D scenes with smooth, evolving details is hard without complex meshes or retraining models. The authors introduce GaussPDE, a method that adds physical equation-based dynamics directly to 3D Gaussian representations, keeping their shapes and colors stable while allowing changes over time. They improve scene quality by carefully organizing the points in 3D space to avoid visual glitches and then use mathematical equations to produce smooth animations that stay true to the scene’s structure. This results in realistic, controllable visual effects in 3D renderings without needing to rebuild the scene from scratch.
What this means in practice
- •For game developers: Create visually smooth and controllable animations in 3D games using Gaussian-based rendering without needing full mesh models or retraining.$Commercial implications: Allows development of advanced graphics engines with PDE-driven effects integrated into 3D Gaussian scenes for more dynamic game visuals.
- •For visual effects artists: Produce stable, dynamic visual effects in 3D scenes without complex geometry pipelines, enabling faster iteration and realistic result control.
Authors
Haoyuan Yue, Fengyuan Ye, Ziyin Li
Abstract
We present GaussPDE, a framework that injects physically structured partial differential equation (PDE) dynamics into pretrained 3D Gaussian scenes without mesh extraction, voxelization, or retraining. Our key observation is that PDE rendering requires not only accurate appearance, but also a reliable discrete computational domain. We therefore first introduce camera-aware regularization during 3DGS reconstruction to suppress camera-near floaters and oversized primitives that would create unstable graph topology. We then construct an active Gaussian graph using covariance-aware distances and opacity, appearance, and boundary-aware conductance, enabling mass-weighted graph Laplacian PDE evolution directly over Gaussian primitives. The evolving scalar PDE state is coupled back to rendering by modifying the direct-current spherical harmonic color coefficients while preserving geometry, opacity, and view-dependent rendering behavior. Experiments on real and synthetic scenes show that GaussPDE produces stable, controllable, and spatially coherent dynamic visualizations, with reduced cross-boundary leakage compared with baselines.