发表机构
Westlake University; The Chinese University of Hong Kong, Shenzhen（西湖大学; 香港中文大学（深圳））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
GaussPDE将物理PDE动力学注入预训练3D高斯场景，通过相机正则化和图拉普拉斯演化实现稳定可控的动态渲染，减少跨边界泄漏。
AI 中文摘要
我们提出了GaussPDE，一个将物理结构化的偏微分方程（PDE）动力学注入预训练的三维高斯场景中的框架，无需网格提取、体素化或重新训练。我们的关键观察是，PDE渲染不仅需要准确的外观，还需要可靠的离散计算域。因此，我们首先在三维高斯泼溅（3DGS）重建过程中引入相机感知的正则化，以抑制相机附近的漂浮物和过大的图元，这些会导致不稳定的图拓扑。然后，我们利用协方差感知的距离以及不透明度、外观和边界感知的电导率构建一个活跃的高斯图，使得质量加权的图拉普拉斯PDE演化能够直接在高斯图元上进行。演化中的标量PDE状态通过修改直流球谐颜色系数耦合回渲染，同时保持几何、不透明度和视图相关的渲染行为。在真实和合成场景上的实验表明，GaussPDE产生了稳定、可控且空间连贯的动态可视化，与基线相比减少了跨边界泄漏。
英文摘要
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.
