Dynamic 3D Gaussian Splatting (3DGS) methods reconstruct time-varying scenes from synchronized multi-camera video using photometric supervision. When a moving object becomes fully occluded from all training cameras, this supervision vanishes: the Gaussians representing it receive no gradient signal and degrade. Existing approaches to incomplete observations in neural reconstruction rely on learned generative priors that prioritize visual plausibility over physical correctness. We propose $\textbf{PersistGS}$, a method that restores object permanence during occlusion by coupling differentiable rigid body simulation with 3D Gaussian Splatting. Our approach decomposes the scene into per-object Gaussians and collision meshes, estimates friction and velocity from the observed pre-occlusion trajectory via differentiable simulation, and uses the resulting SE(3) trajectory to position object Gaussians throughout the occlusion period. Because the predicted trajectory satisfies the governing equations of rigid body dynamics, it faithfully captures contact events (bounces, friction-based deceleration, direction changes) that kinematic extrapolation cannot model. We introduce a centroid silhouette loss that isolates positional gradients from appearance noise, yielding 40% lower trajectory error than photometric supervision. We evaluate using cameras withheld from training that observe the object during its occlusion. Experiments on synthetic scenes show that PersistGS outperforms constant velocity extrapolation by +2.46dB PSNR and comes within 0.19dB of a ground-truth trajectory upper bound.

翻译：动态三维高斯溅射（3DGS）方法通过光度监督从同步多视角视频中重建时变场景。当运动物体被所有训练相机完全遮挡时，光度监督失效：表示物体的高斯体因无法获得梯度信号而退化。现有针对神经重建中不完整观测的方法，依赖学习到的生成先验，其优先考虑视觉合理性而非物理正确性。我们提出$\textbf{PersistGS}$方法，通过将可微刚体模拟与三维高斯溅射耦合，在遮挡期间恢复物体恒存性。该方法将场景分解为每个物体的高斯体和碰撞网格，通过可微模拟从观测到的遮挡前轨迹估计摩擦系数与速度，并利用生成的SE(3)轨迹在遮挡期间定位物体高斯体。由于预测轨迹满足刚体动力学控制方程，它能忠实刻画运动学外推无法建模的接触事件（弹跳、摩擦减速、方向变化）。我们引入质心轮廓损失，从外观噪声中分离位置梯度，使轨迹误差比光度监督降低40%。使用遮挡期间观测物体的训练排除相机进行评估。合成场景实验表明，PersistGS比匀速外推方法PSNR提升+2.46dB，且仅比真实轨迹上界低0.19dB。